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 (uv)' = u'v + uv'.

Front

What is the chain rule in differentiation?

Back

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

Front

What is the quotient rule in differentiation?

Back

If u and v are functions of x, then (u/v)' = (u'v - uv')/v².

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

What is the derivative of x^n?

Back

The derivative of x^n is nx^(n-1).