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Computing Derivatives

Computing Derivatives

Example 1

What is the largest the slope of f(x) = sin(x) ever gets? The smallest?

Example 2

What is the largest the slope of f(x) = cos(x) ever gets? The smallest?

Example 3

Let f(x) = -sin(x). Based on the discussion in this section, what is a reasonable formula for f'(x)?

Example 4

Let f(x) = -cos(x). Based on the discussion in this section, is a reasonable formula for f'(x)?

Example 5

Find the derivative of the function. Be sure to use correct notation.

  • f(x) = sin(x)

Example 6

Find the derivative of the function. Be sure to use correct notation.

  • g(z) = cos(z)

Example 7

Find the derivative of the function. Be sure to use correct notation.

  • h(y) = -sin(y)

Example 8

Find the derivative of the function. Be sure to use correct notation.

  • r(k) = -cos(k)
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