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Computing Derivatives

Computing Derivatives

Example 1

The function below is the composition of two other functions. Without rewriting the original function, determine the inside and outside functions.

  •  f(x) = cos(sin x)

Example 2

The function below is the composition of two other functions. Without rewriting the original function, determine the inside and outside functions.

  •  f(x) = ln (x3)

Example 3

The function below is the composition of two other functions. Without rewriting the original function, determine the inside and outside functions.

  • f(x) = 4{7x}

Example 4

The function below is the composition of two other functions. Without rewriting the original function, determine the inside and outside functions.

  • f(x) = (3x2 + 1)4

Example 5

The function below is the composition of two other functions. Without rewriting the original function, determine the inside and outside functions.

  • f(x) = 

Example 6

Find the derivative of the function. These do all require the chain rule.

  • h(x) = (x5 + 4){99}

Example 7

Find the derivative of the function. These do all require the chain rule.

  • h(x) = sin(ln x)

Example 8

Find the derivative of the function. These do all require the chain rule.

  • h(x) = ln(ln x)

Example 9

Find the derivative of the function. These do all require the chain rule.

  • h(x) = e{sin x}

Example 10

Find the derivative of the function. These do all require the chain rule.

  • h(x) = ln x3

Example 11

Let h = (ln x)2.
The following formula for h'(x) comes from applying the chain rule incorrectly. Identify the mistake(s) in the formula.

Example 12

Let h = (ln x)2.
The of the following formulas for h'(x) comes from applying the chain rule incorrectly. Identify the mistake(s) in the formula.

  • h'(x) = 2(ln x)

Example 13

Let h = (ln x)2.
The following formula for h'(x) comes from applying the chain rule incorrectly. Identify the mistake(s) in the formula.

Example 14

Let h = (ln x)2.

  • Find a correct formula for h'(x).
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