Answer
$\frac{dy}{dx}={3}{(3x-4)^{(\frac{-19}{20})}}$
Work Step by Step
given $y=20(3x-4)^\frac{1}{4}{(3x-4)^\frac{-1}{5}}$
$y=20{(3x-4)^{(\frac{1}{4}-\frac{1}{5}})}=20{(3x-4)^{(\frac{1}{20})}}$
on differentiating both sides:
$\frac{dy}{dx}=\frac{d{(20{(3x-4)^{(\frac{1}{20})}}})}{dx}$
$\frac{dy}{dx}=20\frac{1}{20}{(3x-4)^{(\frac{-19}{20})}}{\frac{d(3x-4)}{dx}}$
$\frac{dy}{dx}={3}{(3x-4)^{(\frac{-19}{20})}}$
