derivative of e^{{g}(x}sin(x))

解答

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

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

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

\int_{- \infty}^{12} x e^{\frac{x}{4}} d x

im pl i c i t \frac{d y}{d x}, 3 x^{2} + 2 y^{2} = 30

\frac{\partial}{\partial x} (x^{3} + e^{y})

\frac{d}{d x} (ln (\frac{x}{6}))

\int csc (π x) cot (π x) d x