AP Practice - Derivatives

Front

What is the derivative of sec(x)?

Back

sec(x)tan(x)

Front

Derive y=(Sin(3x))^2

Back

6Cos(3x)Sin(3x)

Front

Find the derivative: y=4e^(x²)

Back

y'=8xe^(x²)

Front

Find dy/dx by Implicit Differentiation: x^3 + y^3 = 36

Back

−x²/y²

Front

What is the derivative of sin(x)?

Back

cos(x)

Front

What is the definition of a derivative?

Back

The derivative of a function measures how the function's output value changes as its input value changes.

Front

What is the power rule for derivatives?

Back

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

Front

What is the product rule for derivatives?

Back

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

Front

What is the quotient rule for derivatives?

Back

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

Front

What is the chain rule for derivatives?

Back

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