Product Rule Derivatives

Front

What is the Product Rule in calculus?

Back

The Product Rule is a formula used to find the derivative of the product of two functions. If u(x) and v(x) are two functions, then the derivative of their product is given by: \( (uv)' = u'v + uv' \)

Front

When do you use the Product Rule?

Back

You use the Product Rule when finding the derivative of a PRODUCT of functions.

Front

Find the derivative of \( y = (x - 1)(x + 2) \).

Back

\( \frac{dy}{dx} = 2x + 1 \)

Front

Find the derivative of \( y = x(3x - 1) \).

Back

\( \frac{dy}{dx} = 3x^2 \)

Front

Find the derivative of \( y = x(x^2 + x + 1) \).

Back

\( \frac{dy}{dx} = 3x^2 \)

Front

Find the derivative of \( y = x(28x^5 + 5x^3 - 16) \).

Back

\( \frac{dy}{dx} = x(28x^5 + 5x^3 - 16) \)

Front

Find the derivative of \( y = 5x^4(4x^2 + 1) \).

Back

\( \frac{dy}{dx} = 20x^6 + 5x^4 \)

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

What is the derivative of \( x^n \)?

Back

The derivative of \( x^n \) is \( nx^{n-1} \).

Front

Find the derivative of \( y = x^2 + 3x + 5 \).

Back

\( \frac{dy}{dx} = 2x + 3 \)