Exponential & Logarithmic Derivatives

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.

Front

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

Back

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

Front

What is the derivative of ln(x)?

Back

The derivative of ln(x) is 1/x.

Front

Write in logarithmic form: 5^2 = 25.

Back

log_5(25) = 2.

Front

Derive y = e^(3x).

Back

The derivative is 3e^(3x).

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the product rule in differentiation?

Back

The product rule states that if u and v are functions of x, then d(uv)/dx = u'v + uv'.

Front

What is the quotient rule in differentiation?

Back

The quotient rule states that if u and v are functions of x, then d(u/v)/dx = (u'v - uv')/v^2.

Front

What is the derivative of a^x where a is a constant?

Back

The derivative of a^x is a^x * ln(a).

Front

What is the derivative of log_a(x)?

Back

The derivative of log_a(x) is 1/(x * ln(a)).