Derivatives

Front

What is the derivative of a constant function f(x) = c?

Back

The derivative of a constant function is 0.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

Find the derivative of f(x) = 7x^3.

Back

f'(x) = 21x^2.

Front

What is the derivative of f(x) = 1 - x^2?

Back

f'(x) = -2x.

Front

What does it mean for a function to have a horizontal tangent line?

Back

A function has a horizontal tangent line where its derivative is equal to 0.

Front

Find dy/dx for y = (x^2 + 1)^3.

Back

dy/dx = 3(x^2 + 1)^2(2x).

Front

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

Back

f'(x) = e^x.

Front

What is the product rule for differentiation?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

Front

Find the derivative of f(x) = sin(x).

Back

f'(x) = cos(x).