Derivatives

Front

What is the derivative of the function f(x) = 4x^8 + 10x^6 + 3x^3?

Back

f'(x) = 32x^7 + 60x^5 + 9x^2.

Front

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

Back

f'(x) = 0.

Front

What is the derivative of the function y = 8x - x^{-2}?

Back

y' = 8 + 2x^{-3}.

Front

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

Back

f'(x) = 4x^3.

Front

Find the derivative of the function f(x) = \frac{1}{x^2}.

Back

f'(x) = -2x^{-3}.

Front

What is the power rule for differentiation?

Back

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

Front

What is the product rule for differentiation?

Back

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

Front

What is the quotient rule for differentiation?

Back

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

Front

What is the chain rule for differentiation?

Back

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

Front

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

Back

f'(x) = cos(x).