derivative y=e^{2x}arcsin(x)

해법

유도체

y = e^{2 x} arcsin (x)

2 e^{2 x} arcsin (x) + \frac{e ^{2 x}}{1 - x ^{2}}

솔루션 단계

\frac{d}{d x} (e^{2 x} arcsin (x))

곱 규칙 적용:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{2 x}, g = arcsin (x)

= \frac{d}{d x} (e^{2 x}) arcsin (x) + \frac{d}{d x} (arcsin (x)) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (arcsin (x)) = \frac{1}{1 - x ^{2}}

= e^{2 x} \cdot 2 arcsin (x) + \frac{1}{1 - x ^{2}} e^{2 x}

\frac{1}{1 - x ^{2}} e^{2 x} = \frac{e ^{2 x}}{1 - x ^{2}}

= 2 e^{2 x} arcsin (x) + \frac{e ^{2 x}}{1 - x ^{2}}