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Popular >

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

Solution

derivative of

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

Solution

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

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}})

Simplify

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

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

Popular Examples

(d^2)/(dx^2)(x/(x+7))

\frac{d ^{2}}{d x ^{2}} (\frac{x}{x + 7})

tangent of f(x)=x+3/x ,\at x=4 tangent of

f (x) = x + \frac{3}{x}, at x = 4

derivative of (x^2/(x+4))

\frac{d}{d x} (\frac{x ^{2}}{x + 4})

slope ofintercept (15,0),(0,-2)slope intercept

(15, 0), (0, - 2)

integral of (x^2)/(sqrt(36-x^2))

\int \frac{x ^{2}}{36 - x ^{2}} d x

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(1-x^2))
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(1-x^2))