Warm-up: Mixed Derivatives Practice

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Differentiate the function y = 2x^2 (3x - 4).

Back

The derivative is 18x^2 - 16x.

Front

Find f'(2) if f(x) = (x^2 - 3)^4.

Back

f'(2) = 16.

Front

What is the derivative of f(x) = 7?

Back

The derivative is 0.

Front

Differentiate f(x) = \frac{x+1}{x-1}.

Back

The derivative is \frac{-2}{x^2 - 2x + 1}.

Front

What is the power rule for differentiation?

Back

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

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

Differentiate y = 2x^{-1}.

Back

The derivative is -2x^{-2}.

Front

What is the chain rule for differentiation?

Back

If f(g(x)) is a composite function, then the derivative is f'(g(x)) * g'(x).