Derivatives

Front

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

Back

The derivative of a constant function is 0.

Front

Back

y' = 2 + 3x^{-2}

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = nx^{n-1}.

Front

Differentiate f(x) = 7.

Back

f'(x) = 0.

Front

Differentiate f(x) = -4x.

Back

f'(x) = -4.

Front

Differentiate f(x) = (2x + 2)(x - 5)^8.

Back

f'(x) = 8(2x + 2)(x - 5)^7 + 2(x - 5)^8.

Front

What is the product rule for differentiation?

Back

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

Front

Differentiate f(x) = x^3 + 5x^2 - 2x + 1.

Back

f'(x) = 3x^2 + 10x - 2.

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

Differentiate f(x) = 4x^5 + 3x^3 - x.

Back

f'(x) = 20x^4 + 9x^2 - 1.