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Popular >

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

Solution

\frac{d}{d x} (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

y^{''}+8y^'+41y=0,y(0)=2,y^'(0)=-7

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

integral from-1 to 1 of 1/(x^{2/3)}

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

derivative of ((x+1/x)^3)

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

derivative of (x^2/(x^2-16))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 16})

integral of x^9ln(x)

\int x^{9} ln (x) d x

Frequently Asked Questions (FAQ)

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