Question

Differentiate: tcos(t^2) ?

Answer 1

`cos(t^2)-2t^2 sin(t^2)`

Explanation:

Use the product rule and chin rule :

`d/dt (t cos(t^2)) = (d/dt t)times cos(t^2) + t times d/dt (cos(t^2))`
`qquad = 1 times cos(t^2) + t times (-sin(t^2)) times (d/dt t^2)`
`qquad = cos(t^2)-2t^2 sin(t^2)`