For f(x) = cos(4x - 1), find the range of f(x). What should be the domain of f(x)?

Q: For the function f(x) = 4x- 3x +2x +6x +2, find f"(x), the third derivative of f, and f''"(x) = %3D

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Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

Q: Find the indicated derivative. 5x2 f'(x) for f(x) = %3D 9x - 4 f'(x) =|

A: We are solving the problem by The by parts rule of derivative.

Q: Given f(x)=−3x^2−x+15, find f′(−3) using the definition of a derivative

A: We have given a function f(x) First we find f'(x) by using the definition of derivatives.

Q: Given the function g(x) = 2^x , along with the tangent line to the graph at x = 0, may you help me…

A: g(x)=2x  , Tangent line at x=0 Apply definition of derivative g'(x)=limh->0.01g(x+h)-g(x)hReplace…

Q: For the given function, find the first derivative f' f(x) = e* · (3 sin x + cos x) + 4x3

A: Differentiate both sides of the equation, with respect to x using the product rule of derivative to…

Q: For numbers 11-15 Given the function f(x) = cos(5x), 0<x< 2n 11. Determine the first derivative.

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Q: For f(x) = sin(x), write an equation for the tangent line to f(x) at x = π. Sketch a graph of f(x)…

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Q: Given the function f (x) = x³ – 4x² + 5x. Find the open interval(s) where f is concave down, where…

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Q: Use the definition of the derivative to find f'(r). 1. f(x) - 3r - dr +5 3.

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Q: Find f′(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Given a function 'f' of x and find its first derivative . And also find at x=1 tengent line equation…

Q: for the function f(x) = 2 cos(45x)o , determine: the instantaneous rate of change at x = 12. you…

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Q: Given f(x) = -x – 8, find f' (9) using the definition of a derivative. Provide your answer below:…

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Q: Given f(x) = -7x - 2, find f' (5) using the definition of a derivative. Provide your answer below:…

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Q: Find the indicated derivative and simplify. 12 f(X) for f(x) = x² - 1 f'(X)%3D ]

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Q: For what values is the function f(x)= ln(x+1)/x^2+1 continous? Can you please explain how to…

A: If , g(x) is continuous and h(x) is continuous. Then g(x) / h(x) is continuous.where h(x) not equal…

Q: Find an analystic function whose real part is e-x (x sin y-y cos y)

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Q: Use the table to the right to find the given derivative. 2 3 4 f(x) f'(x) 3 1 4 2 d xf(x)] 2 3 4 dx…

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Q: Given function f, find the slope of the tangent line to the graph of f^-1 at the specified point on…

A: The given function is

Q: Find the indicated derivative and simplify. f'(x) for f(x) = x²-5 f'(x) = ]

A: Please see the explanation below

Q: Find the indicated derivative for y=f(x)=9-x^2

A: Answer and explanation is given below...

Q: Use the chain rule to find the derivative of 16 f(x) = 3( – 52° – 9x")" You do not need to expand…

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Q: Use the chain rule to find the derivative of 16 f(x) = 3(8r" - 5z ) * You do not need to expand out…

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Q: Find the point(s) at which the slope of the tangent line is equal to 21. And find the equation of…

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Q: Given f(x) = -x² – 4x – 6, find f' (4) using the definition of a derivative. Provide your answer…

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Q: function f(x)=2x^3-5x^2+3x+2, find the equation of the tangent line at x=1.

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Q: For the f(x) = 1/1-X^2 and g(x)= x^2/1-X^2 A) shows that these functions have the derivative B) what…

A: We need to find relation between f and g.

Q: Find the indicated derivative and simplify. 21x f'(x) for f(x) = x2 - 2 f'(x) =

A: f(x)=21x3x2-2 Note:   Multiple questions are given we are answer with only one question.

Q: The derivative of the function f is defined by f'(x) = x² sin (2x – 1). If f(4) = –1, then use a…

A: we have to find the value of given function at the given point. the solution of this problem is in…

Q: Find the indicated derivative and simplify. 12 f'(x) for f(x) = x2 - 4 %3D f'(x) =D

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Q: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: Find the point(s) at which the slope of the tangent line is equal to 21. And find the equation of…

A: First we differenciate given function and put equal to slope 21 from there we get value of x and…

Q: For the function f(x) = 8x^3-2x^2+2x, Find the equation of the tangent line at x = 2.

A: Please see the answer in Step 2

Q: Given f(x) = 3 x² – 2 vx , which of the following expressions will represent the first step when…

A: Given,          fx=3x2-2xWe know that,          The derivative of a function, fx using the…

Q: For the pair of functions, find the derivative of the composite function f(t(x)) in terms of one…

A: Derivative: f(t)=ett(x)=9x-4f(x)=e9x-4We know,ddx(ex)=ex

Q: I am given the equation f(x)=(4/x)+3. How would I use the definition of the derivative?

A: According to the question, we have to find the derivative using the defination of the expression…

Q: Given the function F(x)= 1/x2 - Use the definition of the derivative to find f'(2)

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Q: Find the indicated derivative and simplify. 21 x f'(x) for f(x) = x2 - 2

A: solution:-f(x)=21x3x2-2using Quotient Rule;ddxg(x)h(x)=h(x)g'(x)-g(x)h'(x)h(x)2and power…

Q: Given the function f(x) = x° – 4x² + 5x, find the open interval(s) where %3D f is concave down, i.e.…

A: Given the function f(x)=x3-4x2+5x, then we have to find the open interval where the function f is…

Q: Find the derivative.

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Q: Given f(x) = 3 cos² (x), write the equation of the line tangent to y f (x) when 3

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Q: for f(x, y) = sin(O 2- Find the third derivative for

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Q: Find the first and second derivatives of the function. 14. f(x)= x to the 7/2+x to the 5/3-x to the…

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Q: For the function f(x) = 10x² – 3x + 5, find the equation of the tangent line at x = 8.

A: We have to find the equation of the tangent line of  f(x)=10x2-3x+5 at x=8.

Q: Given the function f(x)= x³-4x²+5x, find the open intervals where f is concave down, i.e. where the…

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Q: On the graph of f(x)=sinx and the interval [−2π,0), for what value(s) of x does the graph cross the…

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Q: nd the derivative of th

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Q: Given f(x) = v9x – 7, find f' (8) using the definition of a derivative. (Do not include "f' (8) ="…

A: Given f(x)=9x-7

Q: On the graph of f(x) = sin x and the interval 0, 27), for what value of x does the graph cross the…

A: f(x) = sinx Any Function crosses the x- axis when its y- value becomes 0