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Popular >

derivative of y=xarcsin(x)+sqrt(1-x^2)

Solution

derivative of

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

Solution

arcsin (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= arcsin (x)

Popular Examples

(\partial)/(\partial x)(9sin(2x+y))

\frac{\partial}{\partial x} (9 sin (2 x + y))

(\partial)/(\partial x)(x^2y+yz^3+z^5x)

\frac{\partial}{\partial x} (x^{2} y + y z^{3} + z^{5} x)

(6y+2x-7)dx+(4y+6x-1)dy=0,y(-1)=2

(6 y + 2 x - 7) d x + (4 y + 6 x - 1) d y = 0, y (- 1) = 2

d/(d{z)}(({x}^2+{y}^2+{z}^2)^{-1/2}+ln({x}{y}{z}))

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

y^'=12t^2e^{-y}

y^{^{'}} = 12 t^{2} e^{- y}

Frequently Asked Questions (FAQ)

What is the derivative of y=xarcsin(x)+sqrt(1-x^2) ?
The derivative of y=xarcsin(x)+sqrt(1-x^2) is arcsin(x)
What is the first derivative of y=xarcsin(x)+sqrt(1-x^2) ?
The first derivative of y=xarcsin(x)+sqrt(1-x^2) is arcsin(x)