Hello everyone. This lesson we will tell the quotient rule for derivative.
Quotient Rule for Derivative
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| quotient rule derivative |
Let ݂f(x) and ݃g(x) be two functions. Then the derivative of the quotient:
$(frac{f(x)}{g(x)})’=frac{f'(x).g(x)-f(x).g'(x)}{[g(x)]^2}$
This is how the derivative of the quotient is taken. Now let’s reinforce the issue with an example.
Example:
What is the derivative of $(frac{x^3}{e^x})’$
$(frac{x^3}{e^x})’=frac{(x^3)’.e^x-x^3.(e^x)’}{(e^x)^2}$
$=frac{3x^2e^x-x^3e^x}{(e^x)^2}$
$=frac{x^2e^2.(3-x)}{(e^x)^2}$
$=frac{x^2(3-x)}{e^x}$
