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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

2 x^{2} + x + 5

x^{2} lo g_{10} (\frac{1}{x})

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

sin (x) + ln (x^{2}) + e^{2} x

6 x^{\frac{1}{3}}

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