Derivatives Product and Quotient Rule

Front

What is the Product Rule for derivatives?

Back

If \( y = u \cdot v \), then \( y' = u'v + uv' \), where \( u \) and \( v \) are functions of \( x \).

Front

What is the Quotient Rule for derivatives?

Back

If \( y = \frac{u}{v} \), then \( y' = \frac{u'v - uv'}{v^2} \), where \( u \) and \( v \) are functions of \( x \).

Front

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

Back

Using the Quotient Rule, \( y' = \frac{(-6x^2-30x-6)}{(3x^2-3)^2} \).

Front

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

Back

Using the Product Rule, \( y' = 2x + 1 \).

Front

Find the derivative of \( y = \frac{4x^2+3}{2x^2-5} \).

Back

Using the Quotient Rule, \( y' = \frac{-52x}{(2x^2-5)^2} \).

Front

Find the derivative of \( y = \frac{x+2}{x-3} \).

Back

Using the Quotient Rule, \( y' = \frac{-5}{(x-3)^2} \).

Front

Find the derivative of \( g(x) = \frac{3x-2}{x^2+2} \).

Back

Using the Quotient Rule, \( g'(x) = \frac{-3x^2+4x+6}{(x^2+2)^2} \).

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero.

Front

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

Back

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

Front

What is the chain rule?

Back

If \( y = f(g(x)) \), then \( y' = f'(g(x)) \cdot g'(x) \).