Question

What is the derivative of `f(t) = (lnt, -3t^3+5t )`?

Answer 1

`dy/dx=-9t^3+5t`

Explanation:

We have

`x(t)=ln(t)`

`y(t)=-3t^3+5t`
given.So we get

`dx/dt=1/t`

`dy/dt=-9t^2+5`

then

`dy/dx=(dy/dt)/(dx/dt)=(-9t^2+5)/(1/t)=-9t^3+5t`