Question

Find the nth derivative of x2 sinx

Answer 1

Answer:

$y_n=\left(x^2-n^2+n\right)sin\left(x+\frac{n\pi }{2}\right)-2nx\cdot cos\left(x+\frac{n\pi }{2}\right)$

Step-by-step explanation:

Here given y=x²sin(x)=(sinx)x²=u(x)v(x) are the two functions of x

so we got u(x)=sinx

and v(x)=x²

apply Leibnitzs Rule with u and v as function of x

Please find the complete solution in the pic attached

Answer 2

Answer:

To get the nth derivative of the product of 2 functions, we can use Leibniz rule of successive differentiation. Check the below step by step procedure as follows

By Useing Leibnitz theorem.

The nth derivative of sin(x)=sin(n*(pi)/2)

So, the answer should be