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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{1 - x ^{2}} - \frac{x}{1 - x ^{2}}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

Popular Examples

derivative of f(x)=e^x-x^4 derivative of

f (x) = e^{x} - x^{4}

(\partial)/(\partial x)(-xe^x)

\frac{\partial}{\partial x} (- x e^{x})

sum from n=1 to infinity of ln(n/(2n+5))

n = 1 \sum \infty ln (\frac{n}{2 n + 5})

integral of (x^2-x+6)/(x^3+3x)

\int \frac{x ^{2} - x + 6}{x ^{3} + 3 x} d x

(\partial)/(\partial x)((x*y)/(x+y))

\frac{\partial}{\partial x} (\frac{x \cdot y}{x + y})

Frequently Asked Questions (FAQ)

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