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Popular >

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

Solution

derivative of

arcsin (x) + 1 + x^{2}

Solution

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

Graph

Popular Examples

integral from 0 to 5 of (25-x^2)

\int_{0}^{5} (25 - x^{2}) d x

limit as x approaches 0 of 1/x-csc(x)

x \to 0 lim (\frac{1}{x} - csc (x))

integral from 0 to pi of 9x^2sin(1/2 x)

\int_{0}^{π} 9 x^{2} sin (\frac{1}{2} x) d x

(\partial)/(\partial x)(-1/(x^2)+e^{-y})

\frac{\partial}{\partial x} (- \frac{1}{x ^{2}} + e^{- y})

(dy)/(dx)=y(1+x)^{-1}

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

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