Derivatives

Front

What is the derivative of a constant function f(x) = c?

Back

f'(x) = 0, where c is a constant.

Front

Find the derivative of f(x) = -3/4.

Back

f'(x) = 0.

Front

What is the product rule for derivatives?

Back

If f(x) = g(x)h(x), then f'(x) = g'(x)h(x) + g(x)h'(x).

Front

Find the derivative of f(x) = (2x^5)(x^4).

Back

f'(x) = 18x^8.

Front

What is the derivative of a constant function f(x) = 6?

Back

f'(x) = 0.

Front

Find the derivative of f(x) = (2x - 2x^2)(3 + 5x).

Back

f'(x) = (2x - 2x^2)(5) + (3 + 5x)(2 - 4x).

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 derivative of f(x) = (2x^2 + 4) / (x^2).

Back

f'(x) = -\frac{8x}{(x^2)^2}.

Front

What is the power rule for derivatives?

Back

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

Front

Find the derivative of f(x) = x^5.

Back

f'(x) = 5x^4.