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Computing Derivatives

Computing Derivatives

Example 1

Let f(x) = x + 1 and g(x) = x

  • Find f'(x).

Example 2

Let f(x) = x + 1 and g(x) = x.

  • Find g'(x).

Example 3

Let f(x) = x + 1 and g(x) = x.

  • Find f'(x) × g'(x).

Example 4

Let f(x) = x + 1 and g(x) = x.

  • Find (f × g)'(x).

Example 5

Let f(x) = x + 1 and g(x) = x.

  • Must the derivative of the function f × g be equal to the product of f' and g'?

Example 6

Find the derivative of each function. They may not all require the product rule.

  • f(x) = xsin x

Example 7

Find the derivative of each function. They may not all require the product rule.

  • f(x) = excos x

Example 8

Find the derivative of each function. They may not all require the product rule.

  • f(x) = xln x

Example 9

Find the derivative of each function. They may not all require the product rule.

  • g(x) = 5xex

Example 10

Find the derivative of each function. They may not all require the product rule.

  •  g(x) = (logx)(logx)

Example 11

Find the derivative of each function. They may not all require the product rule.

  • g(x) = 5ex

Example 12

Find the derivative of each function. They may not all require the product rule.

  • h(x) = (x2 + 2x)ln x

Example 13

Find the derivative of each function. They may not all require the product rule.

  • h(x) = ln cos x

Example 14

Find the derivative of each function. They may not all require the product rule.

Example 15

Find the derivative of each function. They may not all require the product rule.

  • j(x) = ln x + cos x

Example 16

Find the derivative of f(x) = (x2 + 2)(x3-4).

  • Use the product rule.

Example 17

Find the derivative of f(x) = (x2 + 2)(x3-4).

  • Rewrite f by multiplying the factors together, then take the derivative.

Example 18

  • Find the derivative of

f(x) = x2exsin x

thinking of the function as

f(x) = (x2)(exsin x).

Example 19

Find the derivative of the function

f(x) = x3sin cos x

in two different ways. Give the answer with everything multiplied out (instead of factoring out common factors).

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