Question

y=(√3x-5 -1/√3x-5)^5 differentiate with respect to x

Answer 1

Given:

y=(√3x-5 -1/√3x-5)^5

To find:

y=(√3x-5 -1/√3x-5)^5 differentiate with respect to x

Solution:

From given, we have,

y=(√3x-5 -1/√3x-5)^5

$\dfrac{d}{dx}\left(\left(\dfrac{\sqrt{3x-5}-1}{\sqrt{3x-5}}\right)^5\right)$

applying the chain rule, we get,

$=\dfrac{d}{du}\left(u^5\right)\dfrac{d}{dx}\left(\dfrac{\sqrt{3x-5}-1}{\sqrt{3x-5}}\right)\\\\=5u^4\dfrac{3}{2\left(3x-5\right)\sqrt{3x-5}}$

resubstituting the value, we get,

$=5\left(\dfrac{\sqrt{3x-5}-1}{\sqrt{3x-5}}\right)^4\dfrac{3}{2\left(3x-5\right)\sqrt{3x-5}}\\\\=\dfrac{15\left(\sqrt{3x-5}-1\right)^4}{2\left(3x-5\right)^3\sqrt{3x-5}}$