3.9: Derivatives of Exponential and Log Functions Objective: To find and apply the derivatives of exponential and logarithmic functions.

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Presentation transcript:

3.9: Derivatives of Exponential and Log Functions Objective: To find and apply the derivatives of exponential and logarithmic functions

QUICK REVIEW….. Properties of logs and exponential functions

Derivative of e x Important limit: Proof:

If u is a differentiable function of x, then Examples: Find y’.

Derivative of a x Assume a is positive, and different from 1 Use properties of logs to write a x in terms of e x :

If u is a differentiable function of x, then: Examples: Find the derivative.

At what point on the function y=4 t -5 does the tangent line have a slope of 15?

Derivative of ln x : y=ln x e y =x Use implicit to differentiate:

If u is a differentiable function of x and u>0, then: Examples: Find dy/dx.

Derivative of log a x: Change of Base formula

If u is a differentiable function of x and u>0, then: Examples: Find y’:, for a >0, a ≠ 1

Find the derivative of the following functions.

Find an equation of the tangent line to the graph of the function at the given point.

Power Rule for Arbitrary Real Powers If u is a positive differentiable function of x and n is any real number, then u n is a differentiable function of x and

Logarithmic Differentiation Find the derivative: y=(x-2) x+1 ← Notice x in base and exponent!! No rule for this!

FIND DY/DX