Derivatives of Logs and Exponentials

Front

What is the derivative of the function y = e^x?

Back

y' = e^x

Front

What is the derivative of the function y = a^x, where a is a constant?

Back

y' = a^x ln(a)

Front

Find the derivative of y = ln(x).

Back

y' = \frac{1}{x}

Front

What is the derivative of y = log_a(x)?

Back

y' = \frac{1}{x ln(a)}

Front

Find the derivative of y = e^{g(x)} where g(x) is a function of x.

Back

y' = e^{g(x)} g'(x)

Front

What is the chain rule in differentiation?

Back

If y = f(g(x)), then y' = f'(g(x)) g'(x).

Front

Find the derivative of y = 4e^{x^2}.

Back

y' = 8xe^{x^2}

Front

Find the derivative of y = (e^{(2x+1)})^2.

Back

y' = 4e^{(4x+2)}

Front

What is the product rule in differentiation?

Back

If y = u(x)v(x), then y' = u'v + uv'.

Front

What is the quotient rule in differentiation?

Back

If y = \frac{u(x)}{v(x)}, then y' = \frac{u'v - uv'}{v^2}.