en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arcsin(xy)

Solution

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

Solution

\frac{y + x \frac{d y}{d x}}{1 - x ^{2} y ^{2}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Simplify

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

= \frac{y + x \frac{d y}{d x}}{1 - x ^{2} y ^{2}}

Popular Examples

f(x)=(xe^x)/(x+e^x)

f (x) = \frac{x e ^{x}}{x + e ^{x}}

integral of 4/((x+2)(x-2))

\int \frac{4}{( x + 2 ) ( x - 2 )} d x

y^'=(2cos(2x))/(3+2y),y(0)=-1

y^{^{'}} = \frac{2 cos ( 2 x )}{3 + 2 y}, y (0) = - 1

integral from 0 to 1 of (x-1)/(x^2+3x+2)

\int_{0}^{1} \frac{x - 1}{x ^{2} + 3 x + 2} d x

(\partial)/(\partial x)(ln(x+7y+8z))

\frac{\partial}{\partial x} (ln (x + 7 y + 8 z))

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(xy) ?
The derivative of arcsin(xy) is (y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}
What is the first derivative of arcsin(xy) ?
The first derivative of arcsin(xy) is (y+x\frac{dy)/(dx)}{sqrt(1-x^2y^2)}