Derivatives of

Unit 3: Advanced Derivatives and Applications

Derivative of

In other words, keep the exponent the same and multiply by the derivative of the exponent.

This is a process called differentiation by substitution. (though it may not be necessary for all problems)

Remember: is a constant

EX1: Find of

EX2: Find if

Derivatives of Different Bases:

Exponential functions of a different base are always given the restrictions “for and ”.

Negative values of are effected by an even or odd exponent.

If , then

EX3:

Determine if

EX4: At what point on does the tangent line have slope 21?

Divide by

Take the natural log of both sides

Plug into original function to find

Derivatives of and

For and ,

EX5: find if

EX6: find if

Homework

Page 348 #39-44, 47, 59Page 357 #41-44, 49-51Page 322 #47-50, 73, 74

Complete AP Calculus Practice ProblemsQuiz Friday (A) Quiz Tuesday (F)

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