What is (\partial)/(\partial x)(y*arcsin(x/y)) ?

The answer to (\partial)/(\partial x)(y*arcsin(x/y)) is y/(sqrt(y^2-x^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(y*arcsin(x/y))

\frac{\partial}{\partial x} (y \cdot arcsin (\frac{x}{y}))

\frac{y}{y ^{2} - x ^{2}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (arcsin (\frac{x}{y}))

Apply the chain rule:

\frac{1}{1 - ( \frac{x}{y} ) ^{2}} \frac{\partial}{\partial x} (\frac{x}{y})

= \frac{1}{1 - ( \frac{x}{y} ) ^{2}} \frac{\partial}{\partial x} (\frac{x}{y})

\frac{\partial}{\partial x} (\frac{x}{y}) = \frac{1}{y}

= y \frac{1}{1 - ( \frac{x}{y} ) ^{2}} \cdot \frac{1}{y}

Simplify

y \frac{1}{1 - ( \frac{x}{y} ) ^{2}} \cdot \frac{1}{y} : \frac{y}{y ^{2} - x ^{2}}

= \frac{y}{y ^{2} - x ^{2}}

\frac{d}{d x} (sin^{2} (3 x) + cos (5 x^{2}))

\int_{0}^{\infty} e^{- 2 t} d t

\int (x + 2) (x^{2} + 4 x + 2)^{10} d x

\int - 64 d x

n = 1 \sum \infty (- 0.2)^{n - 1}

What is (\partial)/(\partial x)(y*arcsin(x/y)) ?
The answer to (\partial)/(\partial x)(y*arcsin(x/y)) is y/(sqrt(y^2-x^2))