2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim : x- Xo f(x) = Vx + 6 at x = 3

Q: 1. If y = x³ + x - 5 then what is the derivative of y with respect to x?

A: Derivative of a function

Q: Find the derivative of the function.

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Q: Find the derivative of ywith respect to x in the following functions: 18x y (ans.: (3x-2 a) y= and…

A: Derivative of uv uv' = u'v-v'uv2

Q: Find the derivative of the following functions using the long method (limits) (a) x =t-5t- 3 (b) y =…

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Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

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Q: Find the first derivative of y with respect to x for the following :functions b- y = In( 3x .e-*)

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Q: 3. Find the derivative of the function. y = In(t2) – arctan(-

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Q: Find the first order derivative with respect to y of the function u = log(x + x² – y2)

A: Using derivatives.

Q: 1. Use the definition of the derivative to find the derivative of the following functions. 1 (b)…

A: use definition of derivative to find the derivative of the following functions a) fx=x+2 it is known…

Q: Suppose that f'(0) = 2. Find the derivative of the function (e2z – 2x)f(3x) at x = 0.

A: Given that f'(0)=2.Our Aim is to find the derivative of the function (e2x-2x)f(3x)-(i) at x=0.

Q: Find Find the second derivative of the given function. y = In(x² – 1)

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Q: Q1 Find the derivative of the function : f(x)=ex+1-2x³ at x=1.5,with h=0.1, using the central…

A: Numerical differentiation is nothing but to approximate the changing in the function value with…

Q: 2) Let y = xe* and find the first derivative y'. Where is y'>0?What does this tell you about the…

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Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

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Q: A) Find an equation of the line tangent to the function of x2 + (y – x)² = 9 at x = 1. dy 3) Using…

A: A).Givenx2+(y-x)2=9(y-x)2=9-x2y-x=±9-x2y=±9-x2+x -----{1}Taking positive of equation {1}y=9-x2+xNow…

Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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Q: 4. Find the second derivative of Y with respect to x for 4x² + 8y² = 36

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Q: In(x), Sn (4t + et) dt. Find the derivative of F(x). 3.

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

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Q: 1 14) Use the definition of derivative to find dx 3- х.

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Q: 3x g(x)=e* In(4x+1) (с)

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Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

Q: Find the derivative of the function.

A: First, we expand using properties of log

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (t3/2) + √t

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Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: 19.What is the derivative with respect to a of f(x) = 4-32 3z+2 4x-3

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Q: Find the first derivative of with respect to x using the increment method y=3x^2-7x+12

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Q: Suppose h(x): . What is the correct result of the derivative of h with respect to x? 3x · In (5)…

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Q: Y= In (In2 (1-x))re?

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Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. In x 20) у 3

A: Given

Q: 5. a) Find the first order derivative of the following function. y x° In x

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 2. Find derivative of given function defined as follows 2x y = e = ²

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Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: Find the nth derivative of the function y=xlnx at x=1.

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Q: (a) f(x) = (3x² – 5x + 8)35 (b) f(x) = cos(27.x)

A: First I have written the chain rule and then using it find the derivative of given functions.Also…

Q: 15) Determine the 3rd derivative of the function f(x) = 2\x-x³ [T:2]

A: topic - derivatives

Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

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Q: 2. Find the derivative of (a) f(x) = x* + 3x 2+ 4e" 4 (b) f(x) = 2 tan(x)- 2"

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2. Find the derivative of h with respect to u if h = n²u

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Q: 2. Determine the 8th derivative of y with respect to x of the function f(x) = 1 + x2 and find the…

A: fx=11+x2 Differentiate the above function with respect to x. f'x=ddx11+x2=2x1+x22 Again,…

Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

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Q: 10. Find the derivative of y with respect to x. y=(x^(6)lnx)^(4)

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: