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Popular Calculus >

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

Solution

derivative of

y = 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}

Graph

Popular Examples

(\partial)/(\partial v)(uv-1)

\frac{\partial}{\partial v} (uv - 1)

derivative of 4x+(64/x)

\frac{d}{d x} (4 x + \frac{64}{x})

derivative of f(x)=3x-9 derivative of

f (x) = 3 x - 9

limit as x approaches 3 of (x^2-2x+1)/2

x \to 3 lim (\frac{x ^{2} - 2 x + 1}{2})

(3 y/x-8)dx+3dy=0

(3 \frac{y}{x} - 8) d x + 3 d y = 0

Frequently Asked Questions (FAQ)

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