Finding Derivatives of Functions

Front

Differentiate f(x) = 5x^7.

Back

f'(x) = 35x^6.

Front

Find the derivative of the constant function f(x) = 7.

Back

f'(x) = 0.

Front

Differentiate g(x) = (3x - 2)/(x^2 + 2).

Back

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

Front

Find f'(x) if f(x) = \frac{5}{x^2}.

Back

f'(x) = -\frac{10}{x^3}.

Front

Differentiate y = 5x^2 + 3x + 9.

Back

dy/dx = 10x + 3.

Front

What is the power rule for differentiation?

Back

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

Front

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

Back

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

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

Differentiate f(x) = 4x^5 - 3x^3 + 2x - 1.

Back

f'(x) = 20x^4 - 9x^2 + 2.

Front

What is the quotient rule for differentiation?

Back

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