derivative of e^{cos(x}sin(x^2-x))

解答

\frac{d}{d x} (e^{c o s (x)} sin (x^{2} - x))

- e^{c o s (x)} sin (x) sin (x^{2} - x) + e^{c o s (x)} cos (x^{2} - x) (2 x - 1)

求解步骤

\frac{d}{d x} (e^{c o s (x)} sin (x^{2} - x))

使用微分乘法定则:

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

f = e^{c o s (x)}, g = sin (x^{2} - x)

= \frac{d}{d x} (e^{c o s (x)}) sin (x^{2} - x) + \frac{d}{d x} (sin (x^{2} - x)) e^{c o s (x)}

\frac{d}{d x} (e^{c o s (x)}) = - e^{c o s (x)} sin (x)

\frac{d}{d x} (sin (x^{2} - x)) = cos (x^{2} - x) (2 x - 1)

= (- e^{c o s (x)} sin (x)) sin (x^{2} - x) + cos (x^{2} - x) (2 x - 1) e^{c o s (x)}

化简

= - e^{c o s (x)} sin (x) sin (x^{2} - x) + e^{c o s (x)} cos (x^{2} - x) (2 x - 1)

\int (3^{2} + x^{12}) d x

\frac{d}{d x} (x \cdot (ln (x))^{2})

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 4 s + 3 )}

\int 12 x^{\frac{1}{2}} d x

\frac{d}{d x} (lo g_{e} (\frac{1}{x}))