What is (\partial)/(\partial x)((3x)/(sqrt(x^2+2))) ?

The answer to (\partial)/(\partial x)((3x)/(sqrt(x^2+2))) is 6/((x^2+2)sqrt(x^2+2))

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(\partial)/(\partial x)((3x)/(sqrt(x^2+2)))

\frac{\partial}{\partial x} (\frac{3 x}{x ^{2} + 2})

\frac{6}{( x ^{2} + 2 ) x ^{2} + 2}

Solution steps

\frac{\partial}{\partial x} (\frac{3 x}{x ^{2} + 2})

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

3 \cdot \frac{1 \cdot x ^{2} + 2 - \frac{x}{x ^{2} + 2} x}{( x ^{2} + 2 ) ^{2}} : \frac{6}{( x ^{2} + 2 ) x ^{2} + 2}

= \frac{6}{( x ^{2} + 2 ) x ^{2} + 2}

What is (\partial)/(\partial x)((3x)/(sqrt(x^2+2))) ?
The answer to (\partial)/(\partial x)((3x)/(sqrt(x^2+2))) is 6/((x^2+2)sqrt(x^2+2))