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

Derive the function (v/p)^0.5(1-1(bc*a)/(x^2)) with respect to x

Answer

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

Step-by-step explanation

Problem

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

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sqrt{\frac{v}{p}}$ and $g=1-\frac{c\cdot b\cdot a}{x^2}$

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

Unlock this step-by-step solution!

Answer

$\frac{2c\cdot b\cdot a\sqrt{v}}{\sqrt{p}x^{3}}$
$\frac{d}{dx}\left(\sqrt{\frac{v}{p}}\left(1-\frac{ab\cdot c}{x^2}\right)\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.71 seconds