derivative of (sin(2x)^x)

解答

\frac{d}{d x} ((sin (2 x))^{x})

sin^{x} (2 x) (ln (sin (2 x)) + 2 x cot (2 x))

求解步骤

\frac{d}{d x} ((sin (2 x))^{x})

使用指数法则:

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

(sin (2 x))^{x} = e^{x l n (s i n (2 x))}

= \frac{d}{d x} (e^{x l n (s i n (2 x))})

使用连锁律:

e^{x l n (s i n (2 x))} \frac{d}{d x} (x ln (sin (2 x)))

= e^{x l n (s i n (2 x))} \frac{d}{d x} (x ln (sin (2 x)))

\frac{d}{d x} (x ln (sin (2 x))) = ln (sin (2 x)) + 2 x cot (2 x)

= e^{x l n (s i n (2 x))} (ln (sin (2 x)) + 2 x cot (2 x))

e^{x l n (s i n (2 x))} = sin^{x} (2 x)

= sin^{x} (2 x) (ln (sin (2 x)) + 2 x cot (2 x))

\int 3 (5^{1 - 2 x}) d x

\frac{d}{d x} (40 x)

x \to - 2 lim (3 x - 1)

\int \frac{ln ( x ^{2} + 1 )}{x ^{3}} d x

\frac{\partial}{\partial x} (x^{0.25} Y (x)^{0.5})