derivative of 2^{arctan(x})

解答

\frac{d}{d x} (2^{a r c t a n (x)})

\frac{ln ( 2 ) \cdot 2 ^{a r c t a n (x)}}{x ^{2} + 1}

求解步骤

\frac{d}{d x} (2^{a r c t a n (x)})

使用指数法则:

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

2^{a r c t a n (x)} = e^{a r c t a n (x) l n (2)}

= \frac{d}{d x} (e^{a r c t a n (x) l n (2)})

使用连锁律:

e^{a r c t a n (x) l n (2)} \frac{d}{d x} (arctan (x) ln (2))

= e^{a r c t a n (x) l n (2)} \frac{d}{d x} (arctan (x) ln (2))

\frac{d}{d x} (arctan (x) ln (2)) = \frac{ln ( 2 )}{x ^{2} + 1}

= e^{a r c t a n (x) l n (2)} \frac{ln ( 2 )}{x ^{2} + 1}

化简

e^{a r c t a n (x) l n (2)} \frac{ln ( 2 )}{x ^{2} + 1} : \frac{ln ( 2 ) \cdot 2 ^{a r c t a n (x)}}{x ^{2} + 1}

= \frac{ln ( 2 ) \cdot 2 ^{a r c t a n (x)}}{x ^{2} + 1}

\int (x + 1)^{2} e^{- 2 x} d x

\frac{\partial}{\partial x} (cos^{6} (x^{2} y^{9}))

\frac{d}{d x} (3 x^{2} + x y + 2 x + y)

t a y l or cos (x), \frac{π}{2}

\frac{\partial}{\partial y} (x^{4} y - 3 x^{5} y^{2})