I understand the substituation part for f(g(x)), but it says to simplify it and thats the part that I don't understand

Q: Find the derivative.   g(x) = 4^x/x^4

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Q: Find the indicated derivative. 5x2 f'(x) for f(x) = %3D 9x - 4 f'(x) =|

A: We are solving the problem by The by parts rule of derivative.

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: Find the derivative of the f(x) = (x² + 1)³

A: To find the derivative of the function: fx=x2+13

Q: What is the derivative of f(x)=−3? Do not include "f′(x)=" in your answer. For example, if you found…

A: Formula:The derivative of a constant function is zero.

Q: Find the third derivative of the giyen function. (Simplify your answer completely.) f(x) = 5x5 - 6x…

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Q: The degree of the derivative of f(x) = (3–x)'(x – 12)° is

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Q: but f'(x) is never equal to 0. Why

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

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Q: What is the derivative of −3cot(x)−sec(x)? Do not include "f′(x)=" in your answer. For example, if…

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Q: Find the derivative of the function. f(x) = x2(x − 2)7

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Q: Find the derivative. f(x) = 8/ 4x + 7 f'(x) = |

A: Find derivative use Chan rule  And use d/dx(x½)=1/2(x)½

Q: Explain why f(x + h) – f(x - h) 2h should give a reasonable approximation of f'(x) when f'(x) exists…

A: Explain why fx+h-fx-h2h should give a reasonable approximation of f'(x) when f'(x) exists and h is…

Q: Find the indicated derivative using the definition f(x) = 2x4+3x3-2x+7: f'(0)

A: Differentiation is the rate of change in the value of the dependent variable with respect to the…

Q: Find the indicated derivative and simplify. 12 f(X) for f(x) = x² - 1 f'(X)%3D ]

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Q: p(4)(x) = (x² + 9)² f(6)(x) =

A: Given: f""(x)=(x^2+9)^2

Q: Find the indicated derivative and simplify. f'(x) for f(x) = x²-5 f'(x) = ]

A: Please see the explanation below

Q: Find the derivative.  a)f(x)=7(x^2+3)^5

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Find the indicated derivative.f '(x) for f(x) =(x + 3)(x − 4)x2 + 4

A: Given function f(x) = (x+3)(x-4)x2+4differentiating this function with respect to x we get…

Q: What rule should be used in getting the derivative of a.)  f(x) = x^5 b.) h(x) = 3(x + 4)^3 c.)…

A: a. fx=x5 The rule used to get the derivative of given function is, ddxxn=nxn-1 The derivative is,…

Q: Use the chain rule to find the derivative of 16 f(x) = 3( – 52° – 9x")" You do not need to expand…

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Q: Use the chain rule to find the derivative of 16 f(x) = 3(8r" - 5z ) * You do not need to expand out…

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Q: What is the correct numerator for the derivative of f(x)=3x2−x+4 AFTER you have combined f(x+h) and…

A: Answer is given below

Q: Find the derivatives of the function f(x) from the first principle x4+4

A: Here is the solution

Q: Given f(x) = -x² – 4x – 6, find f' (4) using the definition of a derivative. Provide your answer…

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Q: Use the chain rule to find the derivative of 15 f(x) = 4( – 2a + 10x')" You do not need to expand…

A: We can find the derivative using chain rule as below

Q: The derivative of the function has the same sign for all x in its domain, but the function is not…

A: The derivative of the function has the same sign for all x in its domain, but the function is not…

Q: Try to guess a formula for f' (x) where f (x) = 2*. f' (x) =

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Q: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: The function f(æ) can be approximated by L(x) = 3 – 2(x – 4), near x = 4. What is the value of f'…

A: topic -linear approximation

Q: The derivative of f(x) = 5lnx is

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Q: Given f(x) = 2, find f' (1) using the definition of a derivative. x-2 Provide your answer below:…

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Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: I am given the equation f(x)=(4/x)+3. How would I use the definition of the derivative?

A: According to the question, we have to find the derivative using the defination of the expression…

Q: Find the derivative of the function. f(x) =  x3 − 4 x2 + 2

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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: Use the chain rule to find the derivative of 18 f(x) = 2(5æ4 – 2x") You do not need to expand out…

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Q: Find the indicated derivative. f'(x) for f(x) = x + 4)(x – 5) x² + 9 f'(x)

A: Consider the given function, fx=x+4x-5x2+9 First, simplify the denominator as follows,…

Q: 7.) 2Ct f(xJ= x /メ+4 メ+5

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Q: The derivative of 4.x5 is f(x) f(x) = Зх-2

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Q: The derivative of the function has the same sign for all x in its domain, but the function is not…

A: Given, f(x) = x(x2 − 4) To prove f(x) is not one to one

Q: Find the derivative. f(x) = 8/2x + 9 f'(x) =

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Q: Find the derivative and simplify. f(x) = (x12 + 5x4 + 4)(2x3 − 1) f '(x) =

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Q: State the domain of the function and the domain of the derivative. f(x)= 6/2x^2 f'(x)= Domain of…

A: We find f'(x) using the power rule

Q: What is the derivative of f(x) = -3? Do not include "f'(æ) =" in your answer. For example, if you…

A: Given            f(x)=-3

Q: The derivative of the function f(x) = 18 is 1 5x 18 5x + 18 18 5x4 + (x) 18 5x4 (교2) 18 5x4 + (23)

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Q: Shasta was working at differentiating a function p(x) and they found that p'(0) = In Unfortunately,…

A: We will determine the value of the constant a as following.

Q: Use the second derivative   f''(x)=x(x−1)(x−3)^2 to determine where the inflection points of f(x)…

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Q: Find the indicated derivative. f (x) = (x³ – 5x + 2)(x² + x – 7); find f"(x). %3D

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Q: 3 f(x) = (x³ – 8)4 f'(x) :

A: Use Chain Rule with other some basic identities.

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.