Let (-x² when x < 0 f(x) = when x > 0 (a) Is f increasing? (b) Does f have an inverse? If so, what is it?

Q: find the second derivative of the function. \text { 101. } f(x)=\frac{x}{x-1}

A: Given: f(x)=x1-x

Q: Let g(x) = 7-X. Find the derivative of the function g. g'(x) =-In 7 %3D

A:

Q: Find the derivativeof the inverse of the following functions at the specified point on thegraph of…

A: We have to find  the derivativeof the inverse of the following functions at the specified point on…

Q: Find the first derivative f' and the original function ƒ. f"(x) = x³ - 16x + 4, f'(0) = 3, ƒ(0) = 2…

A: Solve the following

Q: Find f'(x) using the definition of the derivative. 1. f(x)=x^3-1

A: We have given f(x) = x3-1 So using definition of derivative  f'(x) = limh→0fx+h-fxh So f(x+h) =…

Q: Find derivative of the function f(x)=x power3 -1/x-1

A: By applying the chain rule and quotient rule we find the derivative of a function.

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

A:

Q: Suppose the derivative of a function  f isf'(x) = (x+ 1) 2 (x -3)5 (x -6)4. On what interval f  is…

A: f(x) will be increasing if f'(x)&gt;0    We first find the zeros of f'(x) They are x=-1 , 3, 6

Q: Given f(x) = x² + 1, x 2 0, Find the derivative of the inverse at the point (5, 2) (do not find f-1)

A: Let's find.

Q: Use mathematical induction to prove that the derivative of f (x) = x^n equals nx^(n-1) whenever n is…

A: Given: P(n) be the statement derivative of f(x)=xn is equal to nxn-1, where n is a positive integer.

Q: find the derivative  f(x)=x3(x2-1/x2+1)

A: Given:The function f(x) = x3 (x2 − 1)/ (x2 + 1)

Q: x4 -5 7) f(x) = In %3D

A: fx=lnx4-5x first, simplify the function  f(x)=lnx4x-5x f(x)=lnx3-5x now take derivative

Q: The fourth derivative of f(x) * f(x) = 2/√√x is 105/8 x-9/2 O True O False

A:

Q: Find (f-)'(a). f(x) = 4 + x2 + tan(Tx/2), -1 < x < 1, a = 4 %3D (F-1)'(a) =

A:

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: he derivative to determine whether the function is strictly monotonic on its entire domain and…

Q: Differentiate  f and find the domain of f f(x)  =   x / ( 1 -  ln (x-1 ))

A: Given: fx=x1-lnx-1 we know that domain of given function is  1-lnx-1≠0lnx-1≠1…

Q: Give the derivative formula for the function g(x) 2.1X 2 g '(x)

A: The given function is

Q: Find the derivative of the function. g(x) = (1 + 5x)5(4 + x – x²)7 - g'(x)

A:

Q: Use the Derivative of the Inverse Theorem to calculate g'(x), where g is the inverse of f. f(x) x +…

A:

Q: Let f be a function defined by f(x) = ln(3 − 2x). What is the maclaurin function expression of the…

A:

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: f(x)=x3-6x2+12x

Q: Give the derivative formula for the function. g(x) = 2.1* + g'(x) =

A:

Q: 3. Find the derivative of f(x) = 5x - 7 using the formula h f(x+h)-f(x) h

A:

Q: Use the Product Rule to find the derivative of the function. g(x) = (x2 - 2x + 5)(x³ - 6) g'(x) =

A:

Q: Let f(x) = }x² – x³. Find the value(s) of x if the second derivative f" (x) equals zero.

A: Use the formula, ddx(xn)=nxn-1 to calculate the derivative. Differentiate f(x) with respect to x to…

Q: Find the derivative of the algebraic function.

A: Differentiation is the process of finding the rate of change of one variable with respect to another…

Q: Use the Generalized Power Rule to find the derivative of the function. f(x) = (x6 + 1)5 f'(x)

A:

Q: Let f(x) = 4 −(1/3)x3 . Determine the derivative (f -1)'(x) of the inverse function to f.

A:

Q: Evaluate the derivative of f(x)=√x2-1, using the formula:

A: Given f(x)=x2-1

Q: Let f and g be the functions defined for x > 0 by f(x) = (Væ)* and g(x) = (Vx)** Which function is…

A: According to the given information, Consider the function f and g defined as:

Q: Suppose f is a one-to-one differentiable function, and its inverse function f-l is also…

A: Given that f is a one-one differentiable function and its inverse function is also differentiable.…

Q: Let f(x) = 4 – x³. Determine the derivative (f-1)'(x) of the inverse function to f.

A:

Q: Find the second derivative of the function. In(x) f(x) = + 6x? -4x° – 18xln(x) + 3-6 ln(x) + 12…

A:

Q: Find the derivative: g(x) = 6x² e- X O g'(x) = 6xe (2-x) Og'(x) = -12xe** O g'(x) = 6xe (2-x) O…

A: We have to find derivative of given function.

Q: Find the derivative of the algebraic function. f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)

A: Given information: fx=x3-xx2+2x2+x-1

Q: the derivative of the function g(x) In(lx2 +21)

A: We have to find the derivative of g(x)=ln(|x2+2|)

Q: Let f(x) = x-3 Use the definition of derivative to find f'(x). %3D 2C

A: Given : fx = xx-3

Q: Find the fourth derivative of f(x)=3-1.

A: To find the fourth derivative of the function: f(x)=3x-1 Now that the nth derivative of the function…

Q: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

A:

Q: Let f(x)=4-1/3x^3. Determine the derivative (f^-1)'(x) of the inverse function to f.

A: Derivative of inverse function is

Q: Write the first and second derivatives of the function. f(x) = x3 - 6x² + 29x f'(x) f"(x) Use the…

A:

Q: Find the second derivative of f(x)=x^3 + x-5

A:

Q: C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

A: Since you posted two questions here, i can answer only 1. Please reupload second question again.…

Q: say that h'(x)=(x^2-6x-7)/(x-6). Make a sign chart for the first derivative of h(x).

A: Given : h'(x) = (x² - 6x - 7)/(x - 6)

Q: Find the derivative of the inverse of the given function at the specified point on the graph of the…

A: To sketch the graph of the function f(x) and determine the value of the derivative of inverse of the…

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

A: The function f(x)=lnx-3. We have to use the derivative to determine whether the function is strictly…

Q: Use the general power rule to find the derivative of the function. f(x) = (8x-x2)3 f'(x) =…

A:

Q: Find (f-1)(a). f(x) = 5 + x + tan(rx/2), -1 < x < 1, a = 5 (f-1)'(a) =

A:

Q: Use the derivative to determine whether the function is strictly monotonic on its entire domain and…

A:

Q: 3 f(x) = (x³ – 8)4 f'(x) :

A: Use Chain Rule with other some basic identities.