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Popular >

derivative of arcsin(x-y)

Solution

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

Solution

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

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

Simplify

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

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

Popular Examples

integral from-1 to 3 of 3x+1

\int_{- 1}^{3} 3 x + 1 d x

tangent of y=x^2,\at x= 1/3 tangent of

y = x^{2}, at x = \frac{1}{3}

(\partial)/(\partial y)((5(y+2))/((x+2)^2))

\frac{\partial}{\partial y} (\frac{5 ( y + 2 )}{( x + 2 ) ^{2}})

(\partial)/(\partial x)(y^x-ln(x^4y+6x))

\frac{\partial}{\partial x} (y^{x} - ln (x^{4} y + 6 x))

y^{''}+y=-3/4 sin(t)+1/4 sin(3t)

y^{^{''}} + y = - \frac{3}{4} sin (t) + \frac{1}{4} sin (3 t)

Frequently Asked Questions (FAQ)

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