Respuesta :
Given:
The function is:
[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]
To find:
The value of [tex]\dfrac{dy}{dx}[/tex].
Solution:
We have,
[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]
It can be written as
[tex]y=-\dfrac{3}{4}x^{\frac{5}{2}}[/tex] [tex][\because \sqrt[n]x=x^\frac{1}{n}][/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=-\dfrac{3}{4}\times \dfrac{5}{2}x^{\frac{5}{2}-1}[/tex] [tex][\because \dfrac{d}{dx}x^n=nx^{n-1}][/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{5-2}{2}}[/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{3}{2}}[/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}\sqrt{x^3}[/tex]
Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is [tex]-\dfrac{15}{8}\sqrt{x^3}[/tex].
