Derivatives of Logs and Exponentials

Front

What is the derivative of y=ln(u) where u is a function of x?

Back

The derivative is y' = (1/u) * (du/dx).

Front

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

Back

The derivative is y' = e^u * (du/dx).

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y is composed of another function u, then the derivative of y with respect to x is y' = (dy/du) * (du/dx).

Front

What is the product rule in differentiation?

Back

The product rule states that if you have two functions u and v, 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 that is the quotient of two functions u and v, then the derivative is (u/v)' = (u'v - uv')/v².

Front

How do you differentiate a logarithmic function?

Back

To differentiate a logarithmic function y=log_b(u), use the formula y' = (1/(u ln(b))) * (du/dx).

Front

What is the derivative of y=4e^(x^2)?

Back

The derivative is y' = 8xe^(x^2).

Front

What is the derivative of y=ln(3x²-5x)?

Back

The derivative is y' = (6x-5)/(3x²-5).

Front

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

Back

The derivative is y' = 6/((ln(4))(6x+5)).

Front

What is the derivative of f(x) = xe^x?

Back

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