AP CALCULUS AB : PROBLEMS ON FINDING DERIVATIVE OF A FUNCTION

In each case, find f'(x).

Problem 1 :

Solution :

Find the derivative with respect to x using quotient rule.

Problem 2 :

f(x) = 2sin-1(4x3)

Solution :

f(x) = 2sin-1(4x3)

Let u = 4x3.

Now, we have

f(x) = 2sin-1u  and  u = 4x3

Find the derivative with respect to x using the method derivative of a functiuon of function.

Problem 3 :

Solution :

Now, we have

Find the derivative with respect to x using the method derivative of a functiuon of function.

Problem 4 :

f(x) = ln 4x2

Solution :

f(x) = ln 4x2

Use the properties of logarithms on the right side.

f(x) = ln 4 + ln x2

f(x) = ln 4 + 2ln x

Find the derivative with respect to x.

Problem 5 :

Solution :

f(x) = 7csc x

Find the derivative with respect to x.

f'(x) = 7(-csc x ⋅ cot x)

Problem 6 :

f(x) = 5sec2x

Solution :

Let u = sec x.

Now, we have

f(x) = u2 and u = sec x

Find the derivative with respect to x using the method derivative of a functiuon of function.

f'(x) = 2u ⋅ (sec x ⋅ tan x)

f'(x) = 2sec x ⋅ (sec x ⋅ tan x)

f'(x) = 2sec2⋅ tan x

Problem 7 :

f(x) = 4x

We know that

(ax)' = ax ⋅ ln a

where a is a constant.

Solution :

f(x) = 4x ⋅ ln 4

Problem 8 :

f(x) = ln (5x - 4)

Solution :

Let u = 5x - 4.

Now, we have

f(x) = ln u and u = 5x - 4

Find the derivative with respect to x using the method derivative of a functiuon of function.

Problem 9 :

Solution :

Problem 10 :

Solution :

Problem 11 :

Solution :

Problem 12 :

Solution :

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