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Popular >

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

Solution

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

Solution

- \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}}}

Popular Examples

integral of (tan(x))^5

\int (tan (x))^{5} d x

derivative of ln(1+x^3)

\frac{d}{d x} (ln (1 + x^{3}))

tangent of y=x^3-2x+1,(0,1)tangent of

y = x^{3} - 2 x + 1, (0, 1)

integral of x/((x^2+1)^{3/2)}

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

integral from 1 to 2 of (15)/(x^3+4x)

\int_{1}^{2} \frac{15}{x ^{3} + 4 x} d x

Frequently Asked Questions (FAQ)

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)}