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How To Use Chain Rule To Compute Derivatives

The chain rule is the rule to compute derivative of composition functions. It says that

$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$ .

We can also view the chain rule as If $u=u(v)$ and $v=v(x)$ then

$\frac{du}{dx}=\frac{du}{dv}\cdot \frac{dv}{dx}$ .

The videos below give you examples how to use this rule.

How To Use Quotient Rule To Compute Derivatives

Th quotient rule is the rule to compute the derivative of the ratio of two functions. It says that

$\displaystyle \frac{d}{dx }\left(\frac{f}{g}\right)=\frac{\frac{df}{dx}g-f\frac{dg}{dx}}{g^2}$ .

Sometimes it is easier to memorize as

$\displaystyle \left(\frac{f}{g}\right)'=\frac{f'g-fg'}{g^2}$ .

The first video below is a song about quotient rule that will make you easier to memorize this rule. The others, will give you examples how to use this rule.

How To Use Product Rule To Compute Derivatives

The product rule is the rule that enable us to compute the derivative of a product of two functions without simplifying the product first. It states that

$\frac{d}{dx}(fg)=\frac{df}{dx}g+f\frac{dg}{dx}$

Some people feel that memorizing the rule in the form

$(fg)'=f'g+fg'$ or $(uv)'=u'v+uv'$ are easier. The videos below will guide you to use this rule to find the derivatives of a product of two functions.