derivative sin(x)ln(5x)

解答

导数

sin (x) ln (5 x)

cos (x) ln (5 x) + \frac{sin ( x )}{x}

求解步骤

\frac{d}{d x} (sin (x) ln (5 x))

使用微分乘法定则:

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

f = sin (x), g = ln (5 x)

= \frac{d}{d x} (sin (x)) ln (5 x) + \frac{d}{d x} (ln (5 x)) sin (x)

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

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= cos (x) ln (5 x) + \frac{1}{x} sin (x)

\frac{1}{x} sin (x) = \frac{sin ( x )}{x}

= cos (x) ln (5 x) + \frac{sin ( x )}{x}

d er i v a t i v e 2 e^{x^{3}} + 1

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

\frac{\partial}{\partial y} (y^{2} - cos (x y))

\int 2 tan (x) d x

\frac{d}{d x} (- \frac{1}{( 2 x + 8 ) ^{\frac{3}{2}}})