What is the derivative of 2/(sqrt(x^2+7)) ?

The derivative of 2/(sqrt(x^2+7)) is -(2x)/((x^2+7)^{3/2)}

What is the first derivative of 2/(sqrt(x^2+7)) ?

The first derivative of 2/(sqrt(x^2+7)) is -(2x)/((x^2+7)^{3/2)}

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\frac{d}{d x} (\frac{2}{x ^{2} + 7})

- \frac{2 x}{( x ^{2} + 7 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{2}{x ^{2} + 7})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{1}{x ^{2} + 7})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 2 \frac{d}{d x} ((x^{2} + 7)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{2} + 7 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 7)

= - \frac{1}{2 ( x ^{2} + 7 ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{2} + 7)

\frac{d}{d x} (x^{2} + 7) = 2 x

= 2 (- \frac{1}{2 ( x ^{2} + 7 ) ^{\frac{3}{2}}} \cdot 2 x)

Simplify

2 (- \frac{1}{2 ( x ^{2} + 7 ) ^{\frac{3}{2}}} \cdot 2 x) : - \frac{2 x}{( x ^{2} + 7 ) ^{\frac{3}{2}}}

= - \frac{2 x}{( x ^{2} + 7 ) ^{\frac{3}{2}}}

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What is the derivative of 2/(sqrt(x^2+7)) ?
The derivative of 2/(sqrt(x^2+7)) is -(2x)/((x^2+7)^{3/2)}
What is the first derivative of 2/(sqrt(x^2+7)) ?
The first derivative of 2/(sqrt(x^2+7)) is -(2x)/((x^2+7)^{3/2)}