derivative y=3^{cos(2x)}+e^3

解答

导数

y = 3^{c o s (2 x)} + e^{3}

- 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

求解步骤

\frac{d}{d x} (3^{c o s (2 x)} + e^{3})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3^{c o s (2 x)}) + \frac{d}{d x} (e^{3})

\frac{d}{d x} (3^{c o s (2 x)}) = - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

\frac{d}{d x} (e^{3}) = 0

= - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x) + 0

化简

= - 2 ln (3) \cdot 3^{c o s (2 x)} sin (2 x)

\int 7 sin (\frac{θ}{3}) d θ

\frac{\partial}{\partial y} (tan (x^{2} + y))

d er i v a t i v e arcsin (x^{5})

d er i v a t i v e \frac{37500}{1 + 19 e ^{- 0.6 x}}

x \to 0 + lim (e^{x l n (x)})