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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 ( x ^{2} + 2 ) ^{\frac{1}{2}}} \cdot 2 x : \frac{x}{( x ^{2} + 2 ) ^{\frac{1}{2}}}

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

Popular Examples

integral of (sqrt(x)+1/(2sqrt(x)))

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

integral of-cos(x)(2x+1)

\int - cos (x) (2 x + 1) d x

derivative of (ln(x)/(x^9))

\frac{d}{d x} (\frac{ln ( x )}{x ^{9}})

derivative of sec(t)derivative of

sec (t)

limit as x approaches 0-of-6/(x^7)

x \to 0 - lim (- \frac{6}{x ^{7}})

Frequently Asked Questions (FAQ)

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