Differentiation Basics

Front

What is the derivative of f(x) = -5/x^4?

Back

f'(x) = 20/x^5

Front

What is the derivative of f(x) = 7(3x + 4)^5?

Back

f'(x) = 105(3x + 4)^4

Front

What is the derivative of f(x) = (x^2 + 1)^6?

Back

f'(x) = 12x(x^2 + 1)^5

Front

What is the derivative of f(x) = 24x^0.333...?

Back

f'(x) = 8/x^0.666... (or 8/x^(2/3))

Front

What is the derivative of f(x) = (25 - x^2)^0.5?

Back

f'(x) = -x/(25 - x^2)^0.5

Front

Define the power rule of differentiation.

Back

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

Front

What is the chain rule in differentiation?

Back

If f(g(x)) is a composite function, then the derivative is f'(g(x)) * g'(x).

Front

What is the product rule in differentiation?

Back

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

Front

What is the quotient rule in differentiation?

Back

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

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.