derivative of (Ax^2+Bx*sin(x))

解

\frac{d}{d x} ((A x^{2} + B x) \cdot sin (x))

(2 A x + B) sin (x) + cos (x) (A x^{2} + B x)

解答ステップ

\frac{d}{d x} ((A x^{2} + B x) sin (x))

A, B

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = A x^{2} + B x, g = sin (x)

= \frac{d}{d x} (A x^{2} + B x) sin (x) + \frac{d}{d x} (sin (x)) (A x^{2} + B x)

\frac{d}{d x} (A x^{2} + B x) = 2 A x + B

\frac{d}{d x} (sin (x)) = cos (x)

= (2 A x + B) sin (x) + cos (x) (A x^{2} + B x)