derivative of e^{2x}*sin(x^2+5)

解

\frac{d}{d x} (e^{2 x} \cdot sin (x^{2} + 5))

e^{2 x} \cdot 2 sin (x^{2} + 5) + cos (x^{2} + 5) \cdot 2 x e^{2 x}

解答ステップ

\frac{d}{d x} (e^{2 x} sin (x^{2} + 5))

積の法則を適用:

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

f = e^{2 x}, g = sin (x^{2} + 5)

= \frac{d}{d x} (e^{2 x}) sin (x^{2} + 5) + \frac{d}{d x} (sin (x^{2} + 5)) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (sin (x^{2} + 5)) = cos (x^{2} + 5) \cdot 2 x

= e^{2 x} \cdot 2 sin (x^{2} + 5) + cos (x^{2} + 5) \cdot 2 x e^{2 x}