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Implicit differentiation Calculator

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1

Solved example of implicit differentiation

$\frac{d}{dx}\left(\frac{x}{a}=5\right)$
2

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(\frac{x}{a}\right)=\frac{d}{dx}\left(5\right)$
3

The derivative of the constant function ($5$) is equal to zero

$\frac{d}{dx}\left(\frac{x}{a}\right)=0$
4

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{a\frac{d}{dx}\left(x\right)-x\frac{d}{dx}\left(a\right)}{a^2}=0$
5

Multiply both sides of the equation by $a^2$

$a\frac{d}{dx}\left(x\right)-x\frac{d}{dx}\left(a\right)=0a^2$
6

Any expression multiplied by $0$ is equal to $0$

$a\frac{d}{dx}\left(x\right)-x\frac{d}{dx}\left(a\right)=0$
7

The derivative of the constant function ($a$) is equal to zero

$a\frac{d}{dx}\left(x\right)+0x=0$
8

Any expression multiplied by $0$ is equal to $0$

$0$
9

$x+0=x$, where $x$ is any expression

$a\frac{d}{dx}\left(x\right)=0$
10

The derivative of the linear function is equal to $1$

$a=0$

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