What is (\partial)/(\partial x)(2xarcsin(x/y)) ?

The answer to (\partial)/(\partial x)(2xarcsin(x/y)) is 2(arcsin(x/y)+x/(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)(2xarcsin(x/y))

\frac{\partial}{\partial x} (2 x arcsin (\frac{x}{y}))

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

Solution steps

\frac{\partial}{\partial x} (2 x arcsin (\frac{x}{y}))

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (x arcsin (\frac{x}{y}))

Apply the Product Rule:

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

f = x, g = arcsin (\frac{x}{y})

= 2 (\frac{\partial}{\partial x} (x) arcsin (\frac{x}{y}) + \frac{\partial}{\partial x} (arcsin (\frac{x}{y})) x)

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

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

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

Simplify

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

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

y = x^{- 3}, 1 \leq x \leq 5

y = \frac{- 1}{3 sin ^{3} ( x )}

\int (3 t) d t

\int x + tan (x) d x

x \to \infty lim (\frac{3 x ^{2} + 5 x ^{3}}{2 x ^{2} - 3 x})

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