derivative of 4x^4y^3+cos(x^2)

解

\frac{d}{d x} (4 x^{4} y^{3} + cos (x^{2}))

4 (4 x^{3} y^{3} + 3 y^{2} \frac{d y}{d x} x^{4}) - sin (x^{2}) \cdot 2 x

解答ステップ

\frac{d}{d x} (4 x^{4} y^{3} + cos (x^{2}))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{4} y^{3}) + \frac{d}{d x} (cos (x^{2}))

\frac{d}{d x} (4 x^{4} y^{3}) = 4 (4 x^{3} y^{3} + 3 y^{2} \frac{d y}{d x} x^{4})

\frac{d}{d x} (cos (x^{2})) = - sin (x^{2}) \cdot 2 x

= 4 (4 x^{3} y^{3} + 3 y^{2} \frac{d y}{d x} x^{4}) - sin (x^{2}) \cdot 2 x