7. The function f(x) = x+7 is one-to-one. a. Find an equation for f (x), the inverse function. b. Verify that your equation is correct by showing that f(f (x)) = x and f' (f(x)) = x.

Q: In the given question as follows/, find the second derivative of the function.   f (x) = (3 +…

A: f(x)=(3+2x)e-3x

Q: 4) f(x) e**+6x

A: If F(x) = f(g(x)) , then F'(x)= f'(g(x)).g'(x). dexdx=ex dxndx=n.xn-1. Quotient Rule of…

Q: 4. Determine the derivative of the function with respect to x. 8sin?(x² + 2) y = 4tan²(x² + 2)

A:

Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

A:

Q: Find the derivative of the inverse function s(x) if f(x) = -x+ 1 1 r + 1

A:

Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

Q: (14 Find the derivative of the function 7 (^ Y = x²+3 15 x²-3

A: Find the derivative of the function  y= [(x2+3)/(x2-3)]5

Q: 1. Find the derivative of the following functions at an arbitrary point x: 8 a. f(x) = x3/2 b. f(x)…

A:

Q: Find the derivative of the function g(x)=(5x^2−3x+1)e^x g'(x)=___

A:

Q: Find the derivative of the given function from the first principle ax2+bx+c

A:

Q: Find the derivative of the function g(x) et 2 – 2x gʻ(x) =

A: We have to find derivative

Q: Find the derivative of the function g(x)=(3x^2−4x+3)e^x g'(x)=

A:

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

A:

Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

Q: Consider the following. x2 f(x) = x + 2 Find the derivative of the function. f'(x) = %3D

A:

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

A: Given:The given function is f(x)=(3+2x)e-3xTo find:The second derivative of function f(x)

Q: Find the derivative of the function.s(x) = e3x − 1/x3 − 1

A: The given function is

Q: Find the SECOND derivative of the given function. (b) g(x) = x+2

A:

Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

A:

Q: Find the second derivative of the function. g(x) = 9/x + e6× In(x) g"(x) = %3D

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x²;…

A:

Q: h(x) = (cos x)(4x²– 3)

A: Explanation of the answer is as follows

Q: 1. Consider the function f ( x ) = 1 + 1/10 x3 + 1/25 x5 .  Select any point ( a , f -1 ( a ) ) on…

A: Given function : f(x)=1+110x3+125x5 To solve the given problem first we need to find the inverse of…

Q: Find the derivative of the function f (x) = /e* – In(x) 12 – 1/x) O (ex12 – 1) O (e2 – 1/x) e? -x)

A:

Q: 1) Find the hundredth derivative of p (x) = (x+ x³ + x")1º (1 + x²)!' (x³ + x³ + x7). Justify your…

A: The given polynomial function is px=x+x5+x7101+x211x3+x5+x7 We have to find the hundredth derivative…

Q: 4) Find the derivative of each function. a. f (x) = In(x² – 4) In e c. f (x) = b. f (x) = x² ln x

A:

Q: f(x) = e*

A:

Q: 8. y (1 + x³)(3 – 2x) 10. y = (x2 + 3)(x² – x + 1

A:

Q: 16. Find the derivative of the following function. 6x f(x) = 5e 7x f'(x) =

A:

Q: If g(3) = −2 and g'(3) = 15, the compute the derivative of g−1(x) at x = −2

A:

Q: 11 8 Find the derivative of the function: y = 3(x – 4)' x-4

A:

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

A: The first derivative of the function f(x) = (x−2)e−3x is calculated as follows.

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

A:

Q: 3. Find the second derivative of f (x) = e²/*° and fully simplify your answer.

A: fx=e2x3

Q: Which of the following is the derivative of the function f (x) = 5x · e*? Of (x) = 5e* Of'(x) = 5e*…

A:

Q: 1 If f(6) = 3, and f'(6) 2 Let f'(x) be the inverse function of f(x). (f ')'(3) = Write the equation…

A:

Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: 1 4. Use the definition of the derivative to compute f'(x) given f(x) = 2x 3

A: Given,          The function is fx=12x-3 .

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

A:

Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

A:

Q: Find the first derivative of the following implicit function: X² + 3xy + y² = 4

A: Given : x2+3xy+y2=4 Lets take first derivative  Take derivative with respect to x. apply the power…

Q: 22. Find the derivative of the following function. f(x) = 14x6 – 34x + e² f'(x) =

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 1 Find the derivative of each function: b) f(x)=(x'+3x² +7)° 2x+1 b) f(x)=- (x+2x)°

A:

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

A: To find out the function.

Q: Find the derivative of the function g(x) et 2 + 3x g'(x) =

A: Given: gx=ex2+3x

Q: Find the first derivative of the following implicit function. x² + 3xy + y² = 4

A: Given : x2+3xy+y2 = 4

Q: 2. f(x) = 2x – 5x%

A:

Q: 7. Find the second derivative of the following function: y = e** +In(7e¯* + 5x³) – 5²× +-

A: