# Basic Differentiation Rules Calculator

## Get detailed solutions to your math problems with our Basic Differentiation Rules step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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### Difficult Problems

1

Solved example of Basic Differentiation Rules

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

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

$2-4\left(\frac{1}{x+2}\right)\left(\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(2\right)\right)$
8

The derivative of the constant function is equal to zero

$2-4\left(\frac{1}{x+2}\right)\frac{d}{dx}\left(x\right)$
9

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

$2-4\frac{1}{x+2}$
10

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

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

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