Higher Derivatives

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# Higher Derivatives - PowerPoint PPT Presentation

Higher Derivatives. If f is differentiable to f’ , then f’ may have its own derivative, f’’ , called the second derivative This is the rate of change in f’ – how fast f’ is changing. Example. If , find f’’. More.

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### Higher Derivatives

If f is differentiable to f’, then f’ may have its own derivative, f’’, called the second derivative

• This is the rate of change in f’ – how fast f’ is changing
Example

If , find f’’

More

Derivative of f’’ is f’’’ – Third Derivative

Derivative of f’’’ is f’’’’ – Fourth Derivative

Etc.

Example

Find y’’’’ or y(4)of

Example

Find D(27)of y = cos x

Acceleration
• Velocity is how fast distance is changing (f’)
• Acceleration is how fast velocity is changing (f’’)
• A particle’s position is given by the function

, find its acceleration at 4.0 sec.

Graph the position, velocity, and acceleration functions and explain.