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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List of Derivative Rules | All Derivative Rules

You can find all the derivative rules below. We wish everyone good work and good lessons...

Below is a list of all the derivative rules.

Constant Rule:

$f(x)=c$ then $f'(x)=0$

Constant Multiple Rule:

$g(x)=c.f(x)$ then $g'(x)=c.f'(x)$

Power Rule:

$f(x)=x^n$ then $f'(x)=nx^{n-1}$

Sum and Difference Rule:

$h(x)=f(x) ± g(x)$ then $h'(x)=f'(x) ± g'(x)$

Product Rule:

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

Quotient Rule:

$h(x)=\frac{f(x)}{g(x)}$ then $h'(x)=\frac{f'(x).g(x)-f(x).g'(x)}{g(x)^2}$

Chain Rule:

$h(x)=f(g(x))$ then $h'(x)=f'(g(x)).g'(x)$

Trig Derivatives:

$f(x)=sin(x)$ then $f'(x)=cos(x)$

$f(x)=cos(x)$ then $f'(x)=-sin(x)$

$f(x)=tan(x)$ then $f'(x)=sec^2(x)$

$f(x)=sec(x)$ then $f'(x)=sec(x).tan(x)$

$f(x)=cot(x)$ then $f'(x)=-csc^2(x)$

$f(x)=csc(x)$ then $f'(x)=-csc(x).cot(x)$

Exponential Derivatives:

$f(x)=a^x$ then $f'(x)=ln(a).a^x$

$f(x)=e^x$ then $f'(x)=e^x$

$f(x)=a^{g(x)}$ then $f'(x)=ln(a).a^{g(x)}.g'(x)$

$f(x)=e^{g(x)}$ then $f'(x)=e^{g(x)}.g'(x)$

Logarithm Derivatives:

$f(x)=log_a(x)$ then $f'(x)=\frac{1}{ln(a).x}$

$f(x)=lnx$ then $f'(x)=\frac{1}{x}$

$f(x)=log_a(g(x))$ then $f'(x)=\frac{g'(x)}{ln(a).g(x)}$

$f(x)=ln(g(x))$ then $f'(x)=\frac{g'(x)}{g(x)}$

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Quotient Rule for Derivative | How to take the derivative of the quotient?

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

Quotient Rule for Derivative

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 $(\frac{x^3}{e^x})'$

$(\frac{x^3}{e^x})'=\frac{(x^3)'.e^x-x^3.(e^x)'}{(e^x)^2}$

$=\frac{3x^2e^x-x^3e^x}{(e^x)^2}$

$=\frac{x^2e^2.(3-x)}{(e^x)^2}$

$=\frac{x^2(3-x)}{e^x}$

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