Differentiate the function y = x + (x5 + 1)10/3.

Q: Find the derivative (f' (x)) of f(x) = Vx + 2 . %3D

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Q: Find the derivative. 2 f(x) = 8√2x +9 f'(x) = [

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Q: 9. f(x) = /5x + 1 %3D

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Q: The derivative of f(x) =3 4 is %3D

A: Consider the given function, fx=4x5 The property of derivative is defined as, ddxxn=nxn-1 Convert…

Q: Find the second derivative of the function.

A: From the given data:

Q: Find the derivative of the function. x2 + 3 y = x² – 3

A: Consider the given function y=x2+3x2-34

Q: find the derivative  f(x)=x+3+4/x

A: The derivative of the function as follows.

Q: Find the average rate of change of f(x)= 3x^2-2x+6 from x1=4 to x2=7

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Q: Find the higher-order derivative. f(4)(x) = (x² + 6)² f(6) (x) =

A: Finding the 6th derivative, given the fourth derivative.

Q: Find the derivative of the function. f(x) = x2(x − 2)7

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Q: 12. h(x) = ln (x + vx² – 1

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Q: Find the derivative of the algebraic function. f(x) = (x2 + 5x + 6)/(x2 − 4)

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Q: Estimate L4 and R4 over [0,7] for the function f(x) = 2x?. (Use decimal notation. Give your answers…

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Q: Find the derivative of the function. +8x+3 10) y = %3D

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Q: compute the derivative f (x) = 7−2x

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Q: Why can't the power rule be used to differentiate the function y = e"?

A: Given

Q: Integrate the function. dx XV 49x -4

A: Given: Let I=∫dxx49x2-4 To Find: To integrate the given function

Q: Find the derivative of the function. y = 2  4√(9 − x2)

A: Given function: y=29-x24

Q: Find the derivative of the function. y = 10(9 – x2)3

A: Find the derivative of the function y=109-x23.

Q: 2x f(x) = +1

A: Our Aim is to find the derivative of the function given below:-f(x)=2xx2+1 -(i)

Q: b. f(x) = 3v2x %3D

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Q: Find the derivative. a) (x-3)(x+2)(x^3) b) 9x^2(10x+4)

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Q: Differentiate the function. y=(4x– 1)* (2 -x³) ² dx

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: Find the first and second derivatives of the function. (6t2 - 4)2 (5t2)

A: Given function: f(t) = (6t2 - 4)2 (5t2) = (36t4 - 48t2 + 16) (5t2) = 180t6 - 240t4 + 80t2 Recall the…

Q: Find the derivative of the function. f(x)= (x2+6/x)5

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Q: f(x) = (x + 2)(2x² – 3) %3D

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Q: Why can't the power rule be used to differentiate the function y = = e"?

A: Because the power rule only works for function raised to a power for example x^3,x^8 etc.. it is not…

Q: Differentiate the function with respect to the independent variable. f(x) = - 8x+ e + e f'(x) = D

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Q: Find the derivative. f(x)x (2x+1)

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Q: Find the second derivative of the function. y = (8x + 5)3

A: Given: y=8x+53 The power rule for derivatives is expressed as ddxxn=nxn-1…

Q: Differentiate. f(x) = excosx

A: Given: fx=excosx we know that ddxu.v=vdudx+udvdx                                              ..1

Q: Find the derivative of the function. y = (x2 − 6)3

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Q: Find the derivative of the function. f(x) = x(2x − 5)3

A: the given function is: f(x)=x2x-53 we have to find the derivative of the given function.   as we…

Q: Find the derivative of the function. F(x) = (x4 + 5x2 – 9)6

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Q: Find the derivative of f(x) = x ^2at x = 3.

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Q: Calculate the derivative. f(x) = (x³ + 2) (x³ + x + 9)

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Q: x = -t4 – 5t – 3 2.

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Q: find the derivative of the function f(x)=8x^2ln8x

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Q: Integrate the function. dx x2 ', x > 8 Vx2 - 64

A: To integrate the given function

Q: Find the derivative. f(x) = 8/2x + 9 f'(x) =

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Q: Find the derivative of the function f(x) = 9x-³ + x² + 14. f'(x) = %3D

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Q: Find the derivative of the function. f(x) = x2 + 5 − 3x−2

A: Known fact: ddxxn=nxn-1ddxf±g=dfdx±dgdxddxk=0   where k is constant

Q: Differentiate the function ln(x2+y2)+2arctan y/x=0 implicitly.

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Q: Find the derivative of the function. F(x) = (xª + 7x² – 3)4

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Q: Find the derivative. y = 5x(2 – x³)* %3D

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Q: Differentiate the function y=(1−x)3 without using the chain rule.

A: Differentiation: y=(1-x)3 y=1-3x+3x2+x3ddx(xn)=nxn-1

Q: Find the derivative of the function. F(x) = (7x6 + 8x³)4 %3D

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