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Popular >

derivative of x+(1-x^2)^{1/2}

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d x} = 1

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

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

Graph

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Frequently Asked Questions (FAQ)

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