Derivative Rules Flashcard

Front

What is the derivative of f(x) = x^3 + x^2 + 3?

Back

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

Front

What is the derivative of x^n?

Back

The derivative is 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 a function. What is the formula?

Back

If f(x) = g(x)/h(x), then f'(x) = (g'h - gh')/h^2.

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 for derivatives?

Back

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

Front

What is the product rule for derivatives?

Back

If f(x) = u(x)v(x), then f'(x) = u'v + uv'.

Front

What is the chain rule for derivatives?

Back

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

Front

What is the derivative of sin(x)?

Back

The derivative is cos(x).

Front

What is the derivative of cos(x)?

Back

The derivative is -sin(x).