Consider the following functions. f(x) =  1 x ,   g(x) =  3 x + 3 Find  (f + g)(x).

Q: f (x) = (x² – 1)**1

A:

Q: f (x) e1/x x2

A: Given function is fx=e1xx2

Q: Consider the following. g(x) = 8x2 3; h(x) = 1.1 Find the derivative of f(x) g(x) h(x) f'(x)=

A: Given,

Q: What is the derivative of f(x) = x² +x² a +2 where a is a constant ? xa+2

A: We write f(x) using exponents f(x)=x7+x2+a+2xa+2f(x)=x7+x2+(a+2)x-(a+2)

Q: Find the derivative of f(x) = -4x ( 3' *(3"). %D 3+4

A:

Q: Consider the following functions. g(x) = x + 7x h(x) = 7x - 4 x + V7x f(x) 7x - 4 Find the…

A: Given function gx=x+7x                       hx=7x-4                      fx=x+7x7x-4Here we find…

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: Use the first derivative test to determine the relative extreme values of the function. below. a.…

A: We have to determine the relative extreme values of the function using the first derivative test.

Q: Find the first and second derivatives of the function. f(x) = (x2 + 6)5 f'(x) %3D f"(x)

A:

Q: 1. Find the derivative of f(x) if f(x) = x7 + 10x5 – x² – 4

A:

Q: Find the first and the second derivatives of the function. f(x) = (8x + 8)³ f'(x) = f"(x) =| %3D

A:

Q: Find the derivative of the function f(x)=(x2+1)^3(3x+4)^4 at x=−1

A:

Q: Find the derivative of the function described. (Rx5) 3. f (x) = (1 +x + x² + x³ )'³

A:

Q: 2. Find all the derivatives of f, given f(x) = x8 – 5x7 + 4x6 – nx* + 3x3 + 11.

A:

Q: x2 + 6 (a). f(x) x2 – 6

A:

Q: Find the derivative of the function and evaluate f(x) at the given value of x  f(x)=(3x-2)(x^2+3);…

A: Use the derivative of the form f = uv.

Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3

A:

Q: (a) f(x) = V3x + 5 2 (b) f(x) =

A: We need to find the second derivative of the given functions.

Q: Find the derivative of the following functions. 11. f()=(x+3)'(5x+1)° (3x² –4) 12. g(x) = (5x-8) (x²…

A: As per guidelines we can solve only one question at a time, so the first question can be solved as…

Q: 7) calculus homework Q

A:

Q: Find the given higher-order derivative.       f′(x) = x3 − x2/5,  f (3) (x)

A: we have been given: f'(x)=x3-x25 we have to find f(3)(x). that is we have to find the third order…

Q: 3. Find the derivative of the following functions: a. f(x) = (x² + 1)(x³ – 2x² – 1) Activate Windows

A:

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: 1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step…

A: Topic:- function and it's Derivatives

Q: Find the derivative of the algebraic function.

A: The given function is fx=x41-2x+1.

Q: g. f(x)=(1–3x)°(x²-2)°

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Apply the definition of the derivative of a function to find f'(x). a. f(x) = 6x + 4 b. f(x) = x2 -…

A: To find the derivative of the function using the definition of the derivative. (a). Given function…

Q: Find the derivative of the function. g(x) = (2 + (x2 + 1)4)3

A: Consider the provided function, gx=2+x2+143 Find the derivative of the function. Applying the chain…

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 function.

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

Q: Find the derivatives of the following function f(x) from the first principles  (i)x3

A:

Q: Consider the following functions. g(x) = x3 – 9 h(x) = x2 + 7 x3 - 9 x2 +7 f(x) Find the derivative…

A:

Q: 3. Find the derivative of the following function using the formula. S(x + h) – f(x) lim a. f(x) =…

A:

Q: Find the first and second derivatives of the function. f(x) = 11x1 + 6x - x %3D f"(x) = f"(x) =

A:

Q: Find the derivative of the function. f(x) = (x3 + 7x + 5)(3 +1/x2)

A: To determine: Find the derivative of the function.

Q: Find the derivative of f(x) = -4x 3+4 Provide your answer below: f'(x) = D

A:

Q: Find all the higher derivatives of the function f(x) = (4x-5)°. P (x) =] f"(x) = f"(x)=

A: Differentiate above function with respect to x

Q: Find the derivative of the function. f(x)=(x^3+9x+8)(7+1/x^2)

A: fx=x3+9x+87+1x2⇒fx=x3+9x+87+x-2

Q: Find the third derivative of the function. f(x) = (x3 – 8)4 f"'(x) =

A: To find third derivative of function fx=x3-84

Q: Find the derivative of the function. g(x) = 3(4 − 9x)5/6

A:

Q: Find the first and second derivatives of the following functions and use them to sketch a graph. f…

A: Please refer to the image below

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: Find the following derivative 1 g(x) = 2* · (x² + 1)

A:

Q: Find the first and second derivatives of the function.  f(x) = (x2 + 4)5

A: Rule used:The derivative rules are shown below.

Q: Find the derivative of the function f(x) = 8x² – 14x by the definition of derivatives f(x+h)-f(x)…

A: Given function: fx=8x2-14x

Q: Find the first and second derivatives of the given function. f(x) = 8x3 – 5x? + 7 f'(x) = f"(x) %3D

A:

Q: Find the first derivative for the following function. f(x) = 3/7x² – 2 %3D A. f'(x) = 21x(7x² –…

A: Find the derivative

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

A:

Q: find the first and second derivatives of the function f(x) = (x2 + 4)5

A: The given function is f(x)=x2+45.

Q: f '(x)  =        f ''(x)  =

A: From the given equation

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.