Make a sign diagram for the derivative of the function. f(x) = x²(x – 4)2 f'(x) ? v0 f'(x) ?v0 f'(x) ? v0 f'(x)? v0 f'(x) ?0 f'(x)? v0 f'(x) ? v0 X = Find all open intervals of increase and decrease. (Enter your answers using interval notation.) increase decrease

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

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 derivative of the function at the given number. f(x) = 3 – 4x + x², at -1 %3D f'(-1) = %3D

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Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Topic:- calculus

Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: Find the derivative of the function. f(x) = sin(x) cos(5 – x²) f'(x) =

A:

Q: Find the derivative of the function. f(x) = 4 3 VX + 2cos x

A: Here, the given function is: f(x)=4x3+2cos x

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: Determine the derivative of f(x) =2x/x2+1 using the quotient rule and find the equation of the…

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Q: Use the first derivative test to find the location of all local extrema in the interval for the…

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Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A:

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Find the derivative of the function 3 tan (x- 2 1 x y

A: Given:

Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

A:

Q: Find the derivative of the function f(x) = coth−1(x2)

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: What is the derivative of the function with respect to x of (x + 1)³ – æ° -

A: Given : Function x+13 - x3   To find : Derivative of the given function with respect to x?

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)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

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

A: The given derivative function is,

Q: Compute the derivative of the function f(x) = 5x² + 3x at the point x = 4. %3D (Give your answer as…

A: We have to find the derivative at that point

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

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

A:

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 f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: 1, Find the first and the second derivative of f(x): f(x)=x

A:

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

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Find the derivative of the function. f(x) = arctan(3x)

A: We  can make it easier for you.

Q: Find the derivative at the given x-value with the appropriate rule. y=4-18sqrt x at x=4

A:

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: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

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Q: Find the derivative of the function. f(x) = 18 In(x) %3D

A: Derivative Question

Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

A:

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

A:

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

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Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

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

A:

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Find the derivative of f(x) = cot^−1(x^2 + 3)

A:

Q: Determine the derivative of the function with a domain {x |x # 0 and x # + nn, n E R}. sec(x) f(x)…

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Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

A:

Q: Use the definition of derivative to compute f '(0). e-1/x if x * 0 if x - 0 f(x) f '(0) -

A: The definition of the derivative is given by: f'(x)=limh→0f(x+h)-f(x)h⇒f'(0)=limh→0f(h)-f(0)h  ...…

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: Find the derivative of f(x) at the designated value of x (Using Derivative Rules). 3 11. f(x) = x*,…

A: Given :   f(x)=x4 , at x=3/2 f(x)=1/4 , at x=2