Find the derivative of the function using the Power Rule for Functions. y = (x² + 6)²(4x³ – 1)3 dy dx

Q: Find the derivative of the function g(x) = 3arccos(x/2)

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Q: Find the derivative of the function f(x) = 24x arccos(4x) – 6/1 – 16x? f'(x) =

A: To find the derivative of the function

Q: B) Using the definition of derivative, find -if y = dx 1-x

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Q: Find the derivative of the function 1 4. y= 4x +8x dy

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Q: Find the derivative of y with respect to x. 4. (x² - y²)² = 4ay²

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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 derivative of the following functions by applying “Delta Method". Show your complete…

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Q: Find the derivative of the given function. y = In (- 25x² + 3x) y' =D %3D (Турe an exact answer.)

A: Solving by derivative rule

Q: Find the derivative of the function. 4x +6 y-D y'3D

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Q: Use the quotient rule to find the derivative of the following. x2 - 9x + 1 y% = x2 +2 dy dx

A: See attached file for a step by step explanation.

Q: Find the derivative of the given function. y= 2x°-8x +16x+4 dx II

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Q: Use the quotient rule to find the derivative of the function. * + 4 X-9 dy dx I3D

A: This question is related to differentiation, we will use quotient rule to solve it.

Q: Use the Power Rule to compute the derivative: d. X. dx x=-1

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Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Find the derivative of the function. y3 (4x* - 7x +7)* dy dx (Type an expression using x as the…

A: It is given that y=4x4-7x2+74.

Q: Find the derivative of the given function. y= 2x- 13x +35x +5 dy 口 dx %3D

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Q: Find the derivative of y with respect to x if y = (13x - 26x+26) e -8x y =D %3D

A: Explanation of the answer is as follows

Q: Find the derivative of the inverse trig functions. a) y = cos-1 5x b) y = x· arctan x

A: We can solve both the question as below.

Q: Find the derivative of the function y=2x+12x−1 at x=1.

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

A: Given         f(t)=4t2-t

Q: Find the derivative. y = In /x+7 y' = D

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Q: use the Power Rule to compute the derivative.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of the function y = 7-9x. dy dx

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Q: Find the derivative of the function f(x) = 36x arccos(4x) + 9/1 – 16x? f'(x)

A: we will solve using product rule and chain rule of derivative

Q: Find the derivative of the function. y = 7xe−kx

A: Differentiate both sides w.r.t xUse product rule on the right side.

Q: Find the derivative of the function. y = (4x* - 5x² +3)* %3D dy %3D dx (Type an expression using x…

A: We have to solve the differentiation

Q: B. By using the definition of the derivative, find the for: dx 1- f(x) = V %3D 2- f(x) = x -!

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Q: Find the derivative of the given function. y = - 9sin (5x4 - 6) dx ||

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Q: Find the derivative of y with respect to x if y = (12x - 24x + 24) e - 3x. y' =D %3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the derivative of the function. y=-6(8x+8)-6 dy/dx=

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Q: Find the derivative of y=cosine-1(7/x) with respect to x.

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

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3 2x +5 2. y=Va² +x?

A: Using three step rule.

Q: Find the derivative of the function. 9x g(x) = [™ cos(r³]ct Cosx

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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: Find the derivative of y with respect to x. 1. x² + 4y² = 4ay

A: Given:   To find: Derivative of y w.r.t. x:

Q: The derivative of the function y = tan(In(vx² – 6x + 1)) is: %3D

A: Formula:ddx(tan x) = sec2xddx(ln x) =1xddx(xn) =n xn-1

Q: B) Find derivative of the following function d dx 6tanz

A: A detailed solution is given below.

Q: Find the derivative of the following function. y= -58x2-3 %3D dx

A: Simply finding the derivative of the function gives us the answer.

Q: Find the derivative of the function. y = 3x 8 * - 12x - dy dx II

A: Explanation of the answer is as follows

Q: Evaluate the derivative of the following function at the given point. x+ 3x - 5y + 101 = 0: (-3.4)…

A: The objective is to evaluate the derivative of the function at the given point.

Q: y= 4x2-2x - 3

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Q: Find the derivative of the following function. y= -87x2 -9 dy 口 dx

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Q: Find the derivative of the function. y= -3(6x2 +8) -6 dy dx (Type an expression using x as the…

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Q: Find the derivatives of the functions y = x2 sin2 (2x2)

A: Given that : The function is y = x2 sin2 ( 2x2 ) .

Q: Find the derivative of the function. -2 y 14x-6x-9x dy dx

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Q: Use the definition of the derivative to find df/dx. f(x) = x/(1-3x)

A: Given, function

Q: find the derivative of the given function y^4=4xy using implicit differentation

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Q: By using the definition of the derivative, find d/dx   1/(2−x).

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Q: Find the derivative or f'(x) for the following: dx y= x²- 3x + 4 2х-5 (x) = 3x+2

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