Derivative & Integral Formulas

Front

What is the derivative of x^n?

Back

nx^(n-1)

Front

Which of the following is NOT true: Derivatives do not exist at points where the function...

Back

is decreasing.

Front

Find the derivative of f(x) = (x^6 + 4)^5

Back

f '(x) = 30x^5(x^6 + 4)^4

Front

What is implicit differentiation used for in calculus?

Back

To find the derivative of an equation that is not explicitly expressed in terms of one variable.

Front

What is the derivative of x?

Back

1

Front

What is the power rule for derivatives?

Back

If f(x) = x^n, then f'(x) = nx^(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')/v^2.

Front

What is the chain rule for derivatives?

Back

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

Front

What does it mean for a function to be differentiable at a point?

Back

The function has a defined derivative at that point.