Calculus - Log Properties & Derivatives of e^x

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.

Front

Find the derivative of y = 4e^(x²).

Back

y' = 8xe^(x²).

Front

Find the SECOND derivative of f(x) = x² + e^x - cos(x).

Back

f''(x) = 2 + e^x + cos(x).

Front

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

Back

f'(x) = e^x + xe^x.

Front

Find the derivative of y = 5x²e^(3x).

Back

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

Front

What is the product rule in differentiation?

Back

If u and v are functions of x, then the derivative of their product is (uv)' = u'v + uv'.

Front

What is the chain rule in differentiation?

Back

If y = f(g(x)), then the derivative is dy/dx = f'(g(x)) * g'(x).

Front

What is the derivative of e^(g(x))?

Back

The derivative is e^(g(x)) * g'(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 constant function?

Back

The derivative of a constant function is 0.