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Sum rule of differentiation Calculator

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1

Solved example of sum rule of differentiation

$\frac{d}{dx}\left(2x-1\cdot 4\cdot \ln\left(x+2\right)\right)$
2

Multiply $-1$ times $4$

$\frac{d}{dx}\left(2x-4\ln\left(x+2\right)\right)$
3

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(2x\right)+\frac{d}{dx}\left(-4\ln\left(x+2\right)\right)$
4

The derivative of the linear function times a constant, is equal to the constant

$2+\frac{d}{dx}\left(-4\ln\left(x+2\right)\right)$
5

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$2-4\frac{d}{dx}\left(\ln\left(x+2\right)\right)$
6

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$2-4\left(\frac{1}{x+2}\right)\frac{d}{dx}\left(x+2\right)$
7

Apply the formula: $a\frac{1}{x}$$=\frac{a}{x}$, where $a=-4$ and $x=x+2$

$2+\frac{-4}{x+2}\cdot\frac{d}{dx}\left(x+2\right)$
8

The derivative of a sum of two functions is the sum of the derivatives of each function

$2+\frac{-4}{x+2}\left(\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(2\right)\right)$

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

$\frac{-4}{x+2}\cdot\frac{d}{dx}\left(x\right)$
9

The derivative of the constant function ($2$) is equal to zero

$2+\frac{-4}{x+2}\cdot\frac{d}{dx}\left(x\right)$

Any expression multiplied by $1$ is equal to itself

$\frac{-4}{x+2}$
10

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

$2+\frac{-4}{x+2}$

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