Derivative Rules Flashcard

Front

What is the derivative of x^n?

Back

nx^(n-1)

Front

Set up the derivative of y=(3x^4 - 7)(5x^2 + 1)

Back

y' = (3x^4 - 7)(10x) + (12x^3)(5x^2 + 1)

Front

Use the quotient rule to determine the derivative of f(x) = (8x^4 - 60x^2)/(2x^2 - 5)

Back

f'(x) = (8x^4 - 60x^2)/(2x^2 - 5)^2

Front

What is the derivative of a constant, C?

Back

0

Front

Find the derivative of g(x)=(3x-2)/(x^2+2)

Back

g'(x) = (-3x^2 + 4x + 6)/(x^2 + 2)^2

Front

What is the power rule in differentiation?

Back

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

Front

What is the product rule in differentiation?

Back

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

Front

What is the quotient rule in differentiation?

Back

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

Front

What is the derivative of sin(x)?

Back

cos(x)

Front

What is the derivative of cos(x)?

Back

-sin(x)