Derivatives of Natural Log, Exponentials, & Inverse Trig

Front

What is the derivative of the function y = 2^(3x + 4)?

Back

The derivative is y' = 3(ln(2))(2^(3x + 4)).

Front

Find the derivative of y = 5x^2 e^(3x).

Back

The derivative is y' = 5xe^(3x)(3x + 2).

Front

What is the derivative of y = 3ln(x^2 - 3)?

Back

The derivative is y' = \frac{6x}{x^2 - 3}.

Front

What is the derivative of y = (3x^2 + 5)^(1/4)?

Back

The derivative is y' = \frac{3x}{2(3x^2 + 5)}.

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y = f(g(x)), then the derivative y' = f'(g(x)) * g'(x).

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.

Front

What is the derivative of ln(x)?

Back

The derivative of ln(x) is 1/x.

Front

What is the derivative of a^x where a is a constant?

Back

The derivative is a^x ln(a).