derivative 4^{sin(x)}

解答

导数

4^{s i n (x)}

ln (2) \cdot 2^{2 s i n (x) + 1} cos (x)

求解步骤

\frac{d}{d x} (4^{s i n (x)})

使用指数法则:

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

4^{s i n (x)} = e^{s i n (x) l n (4)}

= \frac{d}{d x} (e^{s i n (x) l n (4)})

使用连锁律:

e^{s i n (x) l n (4)} \frac{d}{d x} (sin (x) ln (4))

= e^{s i n (x) l n (4)} \frac{d}{d x} (sin (x) ln (4))

\frac{d}{d x} (sin (x) ln (4)) = 2 ln (2) cos (x)

= e^{s i n (x) l n (4)} \cdot 2 ln (2) cos (x)

化简

e^{s i n (x) l n (4)} \cdot 2 ln (2) cos (x) : ln (2) \cdot 2^{2 s i n (x) + 1} cos (x)

= ln (2) \cdot 2^{2 s i n (x) + 1} cos (x)

sin (2 x) d x + cos (7 y) d y = 0, y (π^{2}) = π^{7}

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

\frac{\partial}{\partial x} (y - x)

x \to 0 lim (\frac{x}{tan ( 3 x )})

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