How do you find the derivative of 4-(x^2)sinx?

May 13, 2018

$- 2 x \sin \left(x\right) - {x}^{2} \cos \left(x\right)$

Explanation:

By using the product rule
$\left(f \left(x\right) \cdot g \left(x\right)\right) ' = f \left(x\right) ' \cdot g \left(x\right) + f \left(x\right) \cdot g \left(x\right) '$

$k \left(x\right) = 4 - {x}^{2} \sin \left(x\right)$
$k ' \left(x\right) = 0 - \left(\left({x}^{2}\right) ' \cdot \sin \left(x\right) + {x}^{2} \cdot \left(\sin \left(x\right)\right) '\right)$
$k ' \left(x\right) = - 2 x \sin \left(x\right) - {x}^{2} \cos \left(x\right)$