derivative of x^{6cos(x})

解答

\frac{d}{d x} (x^{6 c o s (x)})

6 x^{6 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

求解步骤

\frac{d}{d x} (x^{6 c o s (x)})

使用指数法则:

a^{b} = e^{b l n (a)}

x^{6 c o s (x)} = e^{6 c o s (x) l n (x)}

= \frac{d}{d x} (e^{6 c o s (x) l n (x)})

使用连锁律:

e^{6 c o s (x) l n (x)} \frac{d}{d x} (6 cos (x) ln (x))

= e^{6 c o s (x) l n (x)} \frac{d}{d x} (6 cos (x) ln (x))

\frac{d}{d x} (6 cos (x) ln (x)) = 6 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{6 c o s (x) l n (x)} \cdot 6 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{6 c o s (x) l n (x)} = x^{6 c o s (x)}

= 6 x^{6 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

t an g e n t \frac{2}{1 + x ^{2}}

y^{^{'}} + y = e^{3 x}

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

\int \frac{1}{csc ^{4} ( 3 x ) sec ^{2} ( 3 x )} d x

\frac{\partial}{\partial y} (3 x y e^{- x^{2} - y^{2}})