## Task Condition

Find the derivative of the specified order.

$y=x^{2} \cdot \sin (5 x-3), y^{\prime \prime \prime}=?$
## Solution

$y^{\prime}=\left(x^{2} \cdot \sin (5 x-3)\right)^{\prime}=2 x \cdot \sin (5 x-3)+x^{2} \cdot \cos (5 x-3) \cdot 5=$ $=2 x \cdot \sin (5 x-3)+5 x^{2} \cdot \cos (5 x-3)$

$y^{\prime \prime}=\left(y^{\prime}\right)^{\prime}=\left(2 x \cdot \sin (5 x-3)+5 x^{2} \cdot \cos (5 x-3)\right)^{\prime}=$

$=2 \sin (5 x-3)+2 x \cdot \cos (5 x-3) \cdot 5+10 x \cdot \cos (5 x-3)-5 x^{2} \cdot \sin (5 x-3) \cdot 5=$

$=\left(2-25 x^{2}\right) \cdot \sin (5 x-3)+20 x \cdot \cos (5 x-3)$

$y^{\prime \prime \prime}=\left(y^{\prime \prime}\right)^{\prime}=\left(\left(2-25 x^{2}\right) \cdot \sin (5 x-3)+20 x \cdot \cos (5 x-3)\right)^{\prime}=$

$=-50 x \cdot \sin (5 x-3)+\left(2-25 x^{2}\right) \cdot \cos (5 x-3) \cdot 5+20 \cdot \cos (5 x-3)-20 x \cdot \sin (5 x-3) \cdot 5=$

$=-150 x \cdot \sin (5 x-3)+\left(30-125 x^{2}\right) \cdot \cos (5 x-3)$

## Problem Kuznetsov Differentiation 19-7