Find the derivative at each critical point and determine the local extreme values. y = x23(x2 - 4); x 20

Q: Find the derivative of the following function. y = (In |x+4|)7

A: given that  by using chain rule

Q: 2x+1 S(x) = 3x+2,

A: Solution:Given     f(x)=2x+13x+23To find the derivativeFormula:ddx(xn)=nxn-1uv'=vu'-uv'v2

Q: Find the derivative of the given function by definition 6" y 5xar+1 + 3r

A:

Q: Find the derivative of the function and then evaluate at the given point. y= 2x - 5x; (- 1,7)

A:

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: 2 -

A: Chain Rule : (fg(x))' = f'(g(x)).g'(x). d(ax+b)ndx = n.a(ax+b)n-1 dtanxdx = sec2(x)

Q: Find the value of the derivative (if it exists) at the indicated extremum. -4 4/6 3 f(x) = - 3xVx +…

A: To find: The value of the derivative fx=-3xx+2. Formula used: Product rule of differentiation:…

Q: . Get the derivative of the given function. 2. y - In 7x

A: Solving the problem by finding the derivative of the function.

Q: Find all possible functions with the given derivative. y'=-5+7/x^2

A:

Q: Find the derivative of y=-3/(t-2)4

A:

Q: Given the function y=x2cos3x. Find the third-order derivative.

A: To Determine: Third derivative of given function:

Q: Find all possible functions with the given derivative. y = 5x -7x

A: y'=5x2-7x

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Our Aim is to find the second derivative of…

Q: Find the derivative. y = In(t5t)

A: Consider the given equation y=lnt5t and simplify it. Use the logarithmic properties to simplify it.…

Q: 1+cscx 7. h(x)=- 1-csc x

A:

Q: Find the derivative of the function. y In x2+9

A: Given function is: According to chain rule of derivatives:According to the quotient rule:

Q: Find the derivative of the function and then evaluate at the given point. y = 2x - 3x; (- 1,5) f'(x)…

A: f'(-1) = - 7  The detailed solution is as follows below:

Q: find the derivative of the function f(t)=square root of 4t^2-t

A: Given         f(t)=4t2-t

Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Given, f(x)=9x3+1x On differentiating both sides w.r.t x we get:…

Q: Find the value of the derivative (if it exists) at each indicated extremum.       f(x) = −3x√(x + 1)

A:

Q: Find the first derivative of the following implicit function. x3 + y3 + 3 xy2 = 8

A:

Q: Find the derivative of the given functions: 1. y = 6+ 4vx csc(x)

A: If u and v are functions of x, then

Q: Find the derivative. y = In {(x + 1)(2x + 9))

A: Derivative of any function is the rate of change. It represents the amount by which the function is…

Q: Find the derivative of the function and then evaluate at the given point. y= 4x2 - 5x; (– 1,9) f'(x)…

A: The given function is y=4x2-5xThe point is (-1, 9)

Q: Find the derivative.

A: Differentiate above equation with respect to x dydx=ddx{ln(x+1x3+1)}dydx=1(x+1x3+1)ddx(x+1x3+1)…

Q: Find the derivative of the function and then evaluate at the given point. y 3x2-4x; 1,7)

A: To determine the derivative of given function and then evaluate at the point (-1, 7).

Q: Find the derivative of the function given by the equation y2=2px, where p is a parameter.

A: Given equation is Where p is a parameter. This equation is the canonical equation of  a parabola.…

Q: y = e(-x2+3x-4 )

A: Given: y=e-x2+3x-4

Q: find the derivative of the given function F(x)=  x+1/x-1

A: The given function

Q: find the function with the given derivative whosegraph passes through the point P. g'(x) = 1/x2 +…

A: g'(x)=1x2+2x,P(-1,1) Formula ∫xndx=xn+1n+1+C

Q: The 4th derivative of the given function is ソ= 2e2x

A:

Q: Find the derivative of the function. 3.4 q = Vx' + 3x + 3x

A: Given function is

Q: V/2x+3) (x²+1)" 17. f(x)=-

A:

Q: Find the derivative of the function g(x) = (3x² + 3x)e" = (æ),6

A:

Q: Fg(x) = 1 Vx-1

A:

Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = (x +…

A: Given:fx=x+223

Q: Find the value of x for which the derivative is zero of Y =x +4x - 3x – 5

A:

Q: Find the derivative of the irrational function y=2√x−33√x.

A: Given: y=2x-33x

Q: Find the derivative of the function and then evaluate at the given point. y = 2x² - 3x: (-1,5)

A:

Q: Find the derivative with respect to x: y = x3- 3*

A: The given function is: y=x3.3xWe need to find the derivative of y with respect x.Recall the…

Q: Find the derivative of the given function y = (2x+ 5)v4x – 1

A:

Q: - In y = e' sin x

A: We have to find dy/dx of the above equation.

Q: Find the derivative of the function y = x2x+1

A: We have to find derivative of the function: y=x2x+1  In this situation we use logarithmic property…

Q: Find the derivative of the function. G(x) = V1- 9x2 · arccos(3x) G'(x) =

A:

Q: Find the derivative of the following function 1. f(x) = 5x' - 32x + e?

A:

Q: x + y + xy = 21

A: The function is given as , x+y+xy=21 find the second derivative.

Q: Find the derivative by the definition of each of the following functions: - 1- y = 2x2-3x 2- yv1+2x

A:

Q: y" a ||

A: This is the problem of Autonomous Differential equations.

Q: find the following third derivative of y=(3x+2)2

A:

Q: The first derivative of f(x)=e5x^4-6x will be?

A:

Q: X = t-1 2-1

A: Given that x=tt-1,y=t2t2-1. Compute the first derivative.…