Derivatives of exponential functions

Front

What is the derivative of the function y = e^{kx} where k is a constant?

Back

The derivative is y' = ke^{kx}.

Front

How do you find the derivative of a natural logarithm function, such as y = ln(u)?

Back

The derivative is y' = (1/u) * (du/dx), where u is a function of x.

Front

What is the chain rule in differentiation?

Back

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

Front

What is the product rule in differentiation?

Back

The product rule states that if you have two functions u(x) and v(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 you have a function y = u/v, then the derivative is y' = (u'v - uv')/v^2.

Front

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

Back

The derivative is y' = e^{x}.

Front

What is the derivative of the function y = e^{f(x)}?

Back

The derivative is y' = e^{f(x)} * f'(x) using the chain rule.

Front

How do you differentiate y = a^x where a is a constant?

Back

The derivative is y' = a^x * ln(a).

Front

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

Back

The derivative is y' = (2x)/(x^2 - 3) using the chain rule.

Front

What is the derivative of y = e^{5x + ln(x)}?

Back

The derivative is y' = (5 + 1/x)e^{5x + ln(x)} using the chain rule.