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

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

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

The first derivative of (2-x^2)^{1/2} is -x/((2-x^2)^{1/2)}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{1} \frac{1}{x + 1} d x

\int_{0}^{1} (x + x) d x

\int \frac{( 6 - x )}{4 x ^{2} - 12 x + 7} d x

\int \frac{ln ( 2 x )}{2 x ^{2}} d x

\int t (arctan (t)) d t

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