What is (\partial)/(\partial x)(xarcsin(xy)) ?

The answer to (\partial)/(\partial x)(xarcsin(xy)) is arcsin(xy)+(xy)/(sqrt(1-x^2y^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(xarcsin(xy))

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = arcsin (x y)

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

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

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

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

Simplify

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

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

f (x) = \frac{6}{x}

\frac{\partial}{\partial x} ((x - y)^{5})

y = \frac{8}{x ^{2} + 4}, (2, 1)

\int_{1}^{2} \frac{1}{8} + \frac{3}{8} x d x

\frac{d}{d x} ((3 x^{4} - x + 1) (- x^{5} + 4))

What is (\partial)/(\partial x)(xarcsin(xy)) ?
The answer to (\partial)/(\partial x)(xarcsin(xy)) is arcsin(xy)+(xy)/(sqrt(1-x^2y^2))