4/7 Derivative of Exponential and Logarithmic Functions

Front

What is the derivative of the function y=log_4(6x+5)?

Back

Front

Find the derivative of f(x) = xe^x.

Back

The derivative is f'(x) = e^x + xe^x.

Front

What is the slope of the tangent line for f(x)=\frac{e^{(x+1)}}{x+1} at x=-1?

Back

The slope is undefined.

Front

Find the derivative of f(x) = \frac{x^2}{e^x}.

Back

The derivative is f'(x) = \frac{(2x e^x - x^2 e^x)}{(e^x)^2}.

Front

What is the derivative of y=2^{3x+4}?

Back

The derivative is 3(\ln 2)(2^{3x+4}).

Front

Define the derivative of a function.

Back

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y is composed of two functions u and x, then the derivative is dy/dx = (dy/du)(du/dx).

Front

What is the product rule in differentiation?

Back

The product rule states that if u and v are functions of x, then the derivative of their product is (uv)' = u'v + uv'.

Front

What is the quotient rule in differentiation?

Back

The quotient rule states that if u and v are functions of x, then the derivative of their quotient is (u/v)' = (u'v - uv')/v^2.

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.