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\frac{d}{dx}\left(\sqrt{\frac{v}{p}}\frac{ab\cdot c}{x^2}\right)

Derive the function (v/p)^0.5(bc*a)/(x^2) with respect to x

Answer

$\frac{-2\sqrt{v}c\cdot b\cdot a}{x^{3}\sqrt{p}}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\sqrt{\frac{v}{p}}\frac{ab\cdot c}{x^2}\right)$
1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sqrt{\frac{v}{p}}$ and $g=\frac{c\cdot b\cdot a}{x^2}$

$\sqrt{\frac{v}{p}}\cdot\frac{d}{dx}\left(\frac{c\cdot b\cdot a}{x^2}\right)+\frac{c\cdot b\cdot a}{x^2}\cdot\frac{d}{dx}\left(\sqrt{\frac{v}{p}}\right)$

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Answer

$\frac{-2\sqrt{v}c\cdot b\cdot a}{x^{3}\sqrt{p}}$
$\frac{d}{dx}\left(\sqrt{\frac{v}{p}}\frac{ab\cdot c}{x^2}\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.36 seconds