Question

Find the differential coefficient of $\sin {x^3}$.

Answer 1

Hint: Here we will find the differential coefficient using the formulae of differentiations and chain rule.

Complete step-by-step answer:

You have to differentiate $\sin {x^3}$w.r.t x
$\Rightarrow \dfrac{d}{{dx}}\sin {x^3}$
As you know sin differentiation is cos then re-differentiate ${x^3}$
$\Rightarrow \cos {x^3}\dfrac{d}{{dx}}{x^3}$
As you know${x^n}$differentiation is $n.{x^{n - 1}}$
$\Rightarrow \cos {x^3}(3{x^2}) = 3{x^2}\cos {x^3}$
So this is the required answer.
Note: In this type of question always remember the basic differentiation formula. Here students make common mistakes by keeping the answer as $cos {x^3}$ and they do not differentiate ${x^3}$ term. So we have to take care while solving these types of problems.