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)}

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

\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}}

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

4 y^{^{''}} + 9 y^{^{'}} = 0

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

y^{^{''}} + y = 6 sin (2 t) + 4 t cos (2 t)

\frac{d}{d x} (600000 (0.8)^{x})

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)}