Question

Find the differential of y in the function: y=^3√t(t^2+4)?

Answer 1

`dy/dx=(7*t^(4/3))/3 + 4/(3*t^(2/3)`

Explanation:

Multiply cube root of t in the brackets, we get
`y=(t^(2+1/3)) + 4*t^(1/3)`

This gives us
`y=t^(7/3) + 4t^(1/3)`

On differentiating, we get
`dy/dx=(7*t^(4/3))/3 + (4*t^(-2/3))/3`

Which gives,
`dy/dx=(7*t^(4/3))/3 + 4/(3*t^(2/3)`