Answer to Question #188152 in Calculus for VPM

Question

Differentiate the following functions:

y = (t^3 - 5)^1/a

Answer 1

Given function is-

$y=(t^3-5)^{\frac{1}{a}}$

Differentiate with respect to $x-$

$\dfrac{dy}{dt}=\dfrac{1}{a}(t^3-5)^{\frac{1}{a}-1}\times 3t^2\\[9pt]y'(t)=\dfrac{3t^2}{a}(t^3-5)^{\frac{1-a}{a}}$