Use the Product Rule twice to find a formula for (fg)" in terms of f and g and their first and second derivatives.

Q: Use the Power Rule to compute the derivative: da x=1

A: Using the power rule for differentiating x4

Q: Write the function as a composite f (g(x )) and compute the derivative using the Chain Rule.…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: Find the second order derivative of f(x) exsinxcos2x

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Q: 1 Use the power rule to find the derivative of f(x) = Vx 15 f'(x) = %3D

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Q: f(x) = (x² + 2)(e* + 1)

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Q: Find the derivative of f(y)   f1(y) = ?

A: The given is: fy=6tany-y6-8y4y This function can be written as:…

Q: Find the derivative of the function by using the rules of differentiation. , f(x) = 0.7x-1.1 f'(x) =…

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Q: Use the Power Rule to compute the derivative: %3D lx=7

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Q: Use the Product Rule to find the derivative of f. f(x) = csc(x) sec(x) f'(x) = %3D

A: Topic :- Differentiation

Q: Q1. Find the derivative of f(x) = 2x -- by using the definition of derivative.

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Q: Compute the derivative of f(x) = sin2x

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Q: Calculate the derivative of the function y=(x6+2)x  ​(i) using the fact that bx=exlnb and​ (ii) by…

A: Given function is ,

Q: Find the derivative of the function by using the rules of differentiation. 4 f(x) 1 + 400 %3D f'(x)…

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Q: Let f(x) = r - 3z2 - 1. Calculate the derivative

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Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=2 and f'(0)=3, what…

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Q: Find the second derivative by implicit differentiation of 8x² + 16y² = 144 at (1, 1) A. В. -3/4 c.…

A: Given query is to find second derivative of the expression.

Q: Compute the derivative using derivative rules.      y = (x 3 + 3x + 9) -4/3

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Q: Use the definition of the derivative to find the derivative of, f(x)=6

A: topic - derivatives

Q: Use the rules of differentiation to find the derivative of the function.

A: Given,

Q: Compute the derivative using derivative rules  y = (x2 + 9x)- 2

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Q: Find the derivative of f(#) v5-tan(r)

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Q: Calculate the derivative of the function below using the quotient rule. x4 y = Vx + 2x4 f(x) = and…

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Q: · f(x) = sin(In r²) %3D

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Q: Use the rules of differentiation to find the derivative of the function. h(x) = 4Vx + 3Vx %3D h'(x)…

A: Given function is hx=4x+3x3. Solution: Power rule of differentiation states that: ddxxn=nxn-1 Sum…

Q: Find the second derivative using implicit differentiation of x2+8y2=8

A: Given:

Q: Use the rules of differentiation to find the derivative of the function. y = x12

A: The given function is y=x12 rule used: ddxxn=nxn-1

Q: Find the derivative of f(x) = v3x + 1 using the general formula for differentiation.

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Q: Find the derivative of by using the product rule. * (1+ væ³) (x-3 – 2a) y =

A: Consider the provided equation, y=1+x3x-3-2x3 Find the derivative of using the product rule. The…

Q: Find the derivative of f (x) = sin (5x) %3D

A: The given function is f(x)=sin3(5x)                     differentiate with respect to x,

Q: Find the derivative of by using the product rule. * y = (1+ væ³) (x-3 – 2x)

A: To find the derivative of y=1+x3x-3-2x3 using product rule. Solution: Product rule of derivative…

Q: Use the General Power Rule to find the derivative of the function. g(x) = V7- Sx

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Q: Find the derivative of f(x) = x cos x using the product rule.

A: The given function is fx=xcosx.

Q: Calculate the derivative of the function y=(x−1)(x−2)2 without using the product rule for the…

A: Consider the given function y = (x−1)(x−2)2. Simplify the given expression as follows.…

Q: Calculate the derivative of the function y=x(2+3x) without using the product rule.

A: Given function is y=x2+3x. Given function can be written as y=2x+3x2. Power rule of differentiation…

Q: Find the derivative of the function f by using the rules of differentiation. f(x) = x6

A: Power rule: ddxxn=nxn-1

Q: Use the Power Rule to compute the derivative.

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Q: Use the rules of differentiation to find the derivative of the function. h(x) = 4Vx + 3x h'(x) = %3!

A: h'(x)=ddx(h(x))h'(x)=ddx(4x+3x3)h'(x)=ddx(4x)+ddx(3x3) .....( 1)using power rule ddxxn=nxn-1and…

Q: Find the second derivative of the function. f(x) = x x sin(x) %3D f "(x) - !!

A: Given:   fx=x sinx  To find: f"x=?

Q: Use the Chain Rule to find the derivative.

A: First of all, consider the formula for the chain rule and the given function y. Then assume u and v…

Q: Give three different notations for the derivative of ƒ with respectto x

A: Definition used -     Derivative of a function -       It is the rate at which the y value of…

Q: Use the Fundamental Theorem of Calculus to find the derivative. dt

A: We have to find the derivative by fundamental theorem of calculus.

Q: Find the derivative of the function using implicit differentiation.  1.) x³-3x²y+2xy²=12 2.) x²-y²…

A: This question is related to implicit differentiation, We will solve it using given information.

Q: Compute the derivative of f(x) = arcsin(x² e3=).

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Q: Use the rules of differentiation to find the derivative of the function.

A: Use the rules of differentiation to find the derivative of the function.

Q: Find f (x) of f(x)= by using the definition of the x- derivative.

A: Definition of Derivative is given as

Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: Use the rules of differentiation to find the derivative of the function.

A: Given : fx=x19 Differentiate the above function w.r.t 'x" f'x=ddxx19 Recall the formula ddxxn=nxn-1

Q: Find the derivative of the function by using the rules of differentiation. f(x) = 0.006x³ – 0.02x² +…

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Q: Compute the derivative of f (x) : = arcsin(x² e³«).

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Q: Use the rules of differentiation to find the derivative of the function. y = x7

A: Given: The function y=x7, To find: The derivative of given function.