Derivatives

Front

What is the derivative of the function y = 8x - x^(-2)?

Back

y' = x^(-2) + 8x

Front

Find the derivative of f(x) = \frac{1}{x^2}. Hint: rewrite with a negative exponent.

Back

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

Front

What is the derivative of the function f(x) = 1 - x^2?

Back

f'(x) = -2x

Front

Where on the graph would you find a horizontal tangent line?

Back

x = 0

Front

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

Back

f'(x) = 4x^3

Front

Define the derivative in calculus.

Back

The derivative represents the rate of change of a function with respect to a variable.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(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 does it mean for a function to have a horizontal tangent line?

Back

A horizontal tangent line occurs where the derivative of the function is zero.