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人気のある微分積分 >

derivative f(x)=e^xsin(x)

解

導関数

f (x) = e^{x} sin (x)

解

e^{x} sin (x) + cos (x) e^{x}

解答ステップ

\frac{d}{d x} (e^{x} sin (x))

積の法則を適用:

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

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

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

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

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

= e^{x} sin (x) + cos (x) e^{x}

グラフ

人気の例

limit as x approaches 1 of x^2+3

x \to 1 lim (x^{2} + 3)

integral of sqrt(x)-1/2 x

\int x - \frac{1}{2} x d x

(\partial)/(\partial y)(tan(2+2x^2y^4z^2))

\frac{\partial}{\partial y} (tan (2 + 2 x^{2} y^{4} z^{2}))

derivative of (x^2/(10))

\frac{d}{d x} (\frac{x ^{2}}{10})

derivative f(x)=sqrt(1+2x)

d er i v a t i v e f (x) = 1 + 2 x