Basic Derivative Rules (Including Trig)

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Find dy/dx if y = -4x.

Back

dy/dx = -4.

Front

What is the power rule for derivatives?

Back

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

Front

Find the derivative of f(x) = 1/x^2.

Back

f'(x) = -2/x^3.

Front

What is the quotient rule for derivatives?

Back

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

Front

Find the second derivative of f(x) = 2x - 5x^6.

Back

f''(x) = -150x^4.

Front

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

Back

f'(x) = 0.

Front

Find dy/dx if y = sin(x).

Back

dy/dx = cos(x).

Front

Find dy/dx if y = cos(x).

Back

dy/dx = -sin(x).

Front

What is the derivative of f(x) = e^x?

Back

f'(x) = e^x.