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Step-by-step Solution

Derive the function $\sqrt{1-\cos\left(x\right)}$ with respect to x

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Answer

$\frac{1}{2}\left(1-\cos\left(x\right)\right)^{-\frac{1}{2}}\sin\left(x\right)$

Step-by-step explanation

Problem to solve:

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

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{1}{2}\left(1-\cos\left(x\right)\right)^{-\frac{1}{2}}\cdot\frac{d}{dx}\left(1-\cos\left(x\right)\right)$
2

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

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

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Answer

$\frac{1}{2}\left(1-\cos\left(x\right)\right)^{-\frac{1}{2}}\sin\left(x\right)$
$\frac{d}{dx}\left(\sqrt{1-\cos\left(x\right)}\right)$

Main topic:

Differential calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.6 seconds

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