Product Rule & Quotient Rule & Chain Rule (Derivative)

You can find the product rule, quotient rule and chain rule in the derivative below. We wish you good lessons.

Product Rule:

$\frac{d}{dx}(u(x).v(x))=u(x)\frac{dv}{dx}+v(x)\frac{du}{dx}$

Quotient Rule:

$\frac{d}{dx}(\frac{u(x)}{v(x)})=\frac{v(x)\frac{du}{dx}-u(x)\frac{dv}{dx}}{[v(x)]^2}$

Chain Rule:

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

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Product Rule for Derivative | How to take the multiplication derivative?

Hello everyone. This lesson we will tell the product rule for derivative.

Product Rule for Derivative

product rule of derivative

Let f(x) and g(x) be two functions. Then the derivate of the product

$(f(x).g(x))'=f'(x)g(x)+f(x)g'(x)$

We must follow this rule religiously and not succumb to the temptation of writing $(f(x)g(x))'=f'(x)g'(x)$ ; a faulty statement.

Example:

$(x^3.e^x)'=(x^3)'.e^x+x^3(e^x)'$

=$3x^2e^x+x^3e^x$

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