derivative e^{3x}*sin(ln(x))

解答

导数

e^{3 x} \cdot sin (ln (x))

3 e^{3 x} sin (ln (x)) + \frac{e ^{3 x} cos ( ln ( x ) )}{x}

求解步骤

\frac{d}{d x} (e^{3 x} sin (ln (x)))

使用微分乘法定则:

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

f = e^{3 x}, g = sin (ln (x))

= \frac{d}{d x} (e^{3 x}) sin (ln (x)) + \frac{d}{d x} (sin (ln (x))) e^{3 x}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

= e^{3 x} \cdot 3 sin (ln (x)) + \frac{cos ( ln ( x ) )}{x} e^{3 x}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 3 e^{3 x} sin (ln (x)) + \frac{e ^{3 x} cos ( ln ( x ) )}{x}

d er i v a t i v e 4 t^{2} + 3 t + 3

d er i v a t i v e lo g_{10} (2 - x)

\frac{d}{d x} (a \cdot e^{2 x} + b \cdot e^{- 3 x} + c \cdot e^{x})

\frac{d}{d t} (cos^{4} (t) - sin^{4} (t))

d er i v a t i v e y = - x^{3} (3 x^{4} - 2)