Assuming f and g are differentiable functions, determine (fg)'(4) if ƒ(4) = 3. f'(4) = 2, g(4) = -6, and gʻ(4) = 8.

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Find the derivative of f(z) = e2" (3z2- z)

A: Given, f(x)=e2x(3x2-x) Here, when we try to find the derivative of f(x), both chain rule and…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: Find the derivatives of the functions in Exercis

A: We have, f(x)=7+x sec x First, we write the above function in power form. fx=7+x sec x1/2

Q: If f(x)=4/x, find the derivative of f(x) at x=2 using the limit definition of the derivative at a…

A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

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Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

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Q: By using first principle of differentiation find f'(y), if ƒ(y) = Му—N

A: Given: f(y)= My-N According to the first principle of differentiation, the derivative of a function…

Q: find the function with the given derivative whosegraph passes through the point P. ƒ'(x) = 2x - 1,…

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Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: Find the derivative of the function = V(=² – 3)* 6, f(x) at x = 2. %3D f'(2) =

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Q: Compute the derivative using derivative rules.

A: Explanation Given that,  y=(kx+b)-13   Differentiate with respect to x both the sides…

Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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Q: y = x*(1 – In x4)

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Q: or x>0, determine the deriva

A: Consider the given function: Here the objective is to find the derivative of a given function using…

Q: Find the derivative of the function. x + 6 X-6 y' = y = In

A: I have appended the formula used in the solution part of the question.

Q: Find all possible functions f with the given derivative.  f'(x)= ex

A: The given derivative function is,

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: Obtain the derivative of the function y (3 sen(4x))° ( tgʻ(2x)) y = (sec(2x))* – 1

A: This question is based on Trignometric application and diffrentiation of function.

Q: A) Consider the function f(x) whose second derivative is f"(x)=4x+3sin(x). If f(0)=4 and f'(0)=4,…

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Q: Find the derivative of the function .

A: Given a function f(x)=2x3+3 cos x f(x)=2(x)1/3+3 cos x      =2x-1/3+3 cos x We, use the following…

Q: Find the derivative of the function using the slope limit formula. 1 y= 3-х 1. y=(3x+1)2 2. 1 y= 1…

A: Note : As per our company guide lines, we are supposed to answer only one question. Kindly post…

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: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y)=xy, What is…

A: To find the derivative of y with respect to x

Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

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Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A: Given: f(x)=(1-x2) Find the derivative of given function from the left and from the right at x = 1…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 (x2 + 1), x > 0

A: Given that, y=csc-1x2+1

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

A:

Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 (2s + 1)

A: The given function is y=sec-12s+1.

Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…

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Q: are differentiable at a, then prove the sum and product rules for derivatives. If f, 9

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Q: Using appropriate rules, find the derivative of y-r'e + sin(3z+ 5z) 2 3z

A: on solving this we get the

Q: find the 2nd derivative of the function defined implicity by the equation x^1/3+y^1/3=80

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Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

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Q: Find the derivative of the function using the definition of derivative. 1 f(x) V5 + x

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Q: Find the first and second derivatives of the function. f(x) = x/(7+x2) Identify the intervals on…

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Q: Differentiate the functions: 1. y = 3x – Vx 2. y = 2 – 3x – 3. Given the function f(x) = x³ – 5x +…

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Q: Find derivatives of f(x) = {x+- 1 and find the line tangent to it when x = 1

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Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: If the function of x, ƒ(x) = · then, the derivative of f(x) is:

A: We will find the derivative of f(x) as following

Q: the derivative of f(x) = xi at the point x = 4?

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Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

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Q: Find the derivative of the function. f(z) 0.6z-0.4z2 - 0.8 f' (z) -

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Q: Find all possible functions with the given derivative. 1. If y 1, then y %3D 2. If y = a, then y 3.…

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Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

Q: Find the derivative of f(z)=((11z+4)1/2)(e3z).

A: Given function f(z)=11z+412e3z