# Related formulas

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## Basic Derivatives

· Product rule for derivatives

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=[a]$ and $g=[b]$

$\frac{d}{dx}\left(ab\right)=b\frac{d}{dx}\left(a\right)+a\frac{d}{dx}\left(b\right)$
· Derivative of the linear function

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

$\frac{d}{dx}\left(x\right)=1$
· Derivative of the natural logarithm

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 $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)$
$\frac{d}{dx}\left(x^x\right)$

### Main topic:

Logarithmic differentiation

### Time to solve it:

~ 0.04 s (SnapXam)