Question

If$y=3x^{2}t-t^k$, where x and k are constant, find$\frac{dy}{dt}$

Short answer

$\frac{dy}{dt}=3x^2-t^k\log k$

Step-by-step solution

Step 1:Given information

The given expression is$y=3x^{2}t-t^k$

Step 2:Simplification

$y=3x^{2}t-t^k$

Differentiating w.r.t t

$\frac{dy}{dt}=\frac{d}{dt}\left(3x^{2}t\right)-\frac{d}{dt}\left(t^k\right)$

$\Rightarrow \frac{dy}{dt}=3x^2-t^k\log k$