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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

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

= 0 + \frac{1}{( 1 - x ^{2} ) 1 - x ^{2}}

Simplify

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

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Frequently Asked Questions (FAQ)

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