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\frac{d}{dx}\left(\ln\left(arccos\left(\frac{1}{\sqrt{x}}\right)\right)\right)

Find the derivative of ln(arccos(1/(x^0.5)))

Answer

$\frac{\frac{1}{2}}{\sqrt{x^{3}}\sqrt{\frac{-1}{x}+1}arccos\left(\frac{1}{\sqrt{x}}\right)}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\ln\left(arccos\left(\frac{1}{\sqrt{x}}\right)\right)\right)$
1

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

$\frac{d}{dx}\left(arccos\left(\frac{1}{\sqrt{x}}\right)\right)\frac{1}{arccos\left(\frac{1}{\sqrt{x}}\right)}$

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Answer

$\frac{\frac{1}{2}}{\sqrt{x^{3}}\sqrt{\frac{-1}{x}+1}arccos\left(\frac{1}{\sqrt{x}}\right)}$

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$\frac{d}{dx}\left(\ln\left(arccos\left(\frac{1}{\sqrt{x}}\right)\right)\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.77 seconds