What is (\partial)/(\partial x)(arcsin(a/b sin(x))) ?

The answer to (\partial)/(\partial x)(arcsin(a/b sin(x))) is (acos(x))/(sqrt(b^2-a^2sin^2(x)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(arcsin(a/b sin(x)))

\frac{\partial}{\partial x} (arcsin (\frac{a}{b} sin (x)))

\frac{a cos ( x )}{b ^{2} - a ^{2} sin ^{2} ( x )}

Solution steps

\frac{\partial}{\partial x} (arcsin (\frac{a}{b} sin (x)))

Simplify

arcsin (\frac{a}{b} sin (x)) : arcsin (\frac{a sin ( x )}{b})

= \frac{\partial}{\partial x} (arcsin (\frac{a sin ( x )}{b}))

Treat

a, b

as a constant

Apply the chain rule:

\frac{1}{1 - ( \frac{a s i n ( x )}{b} ) ^{2}} \frac{\partial}{\partial x} (\frac{a sin ( x )}{b})

= \frac{1}{1 - ( \frac{a s i n ( x )}{b} ) ^{2}} \frac{\partial}{\partial x} (\frac{a sin ( x )}{b})

\frac{\partial}{\partial x} (\frac{a sin ( x )}{b}) = \frac{a cos ( x )}{b}

= \frac{1}{1 - ( \frac{a s i n ( x )}{b} ) ^{2}} \cdot \frac{a cos ( x )}{b}

Simplify

\frac{1}{1 - ( \frac{a s i n ( x )}{b} ) ^{2}} \cdot \frac{a cos ( x )}{b} : \frac{a cos ( x )}{b ^{2} - a ^{2} sin ^{2} ( x )}

= \frac{a cos ( x )}{b ^{2} - a ^{2} sin ^{2} ( x )}

\frac{48}{s ^{5}}

\int e^{2 x^{3} - 1} x^{2} d x

\int 3 cos^{4} (x) d x

x \to 0 lim (\frac{x ^{2} - 1}{x + 1})

\int \frac{8}{3 cos ( 2 x ) + 1} d x

What is (\partial)/(\partial x)(arcsin(a/b sin(x))) ?
The answer to (\partial)/(\partial x)(arcsin(a/b sin(x))) is (acos(x))/(sqrt(b^2-a^2sin^2(x)))