What is the derivative of x/(3sqrt(1+x^2)) ?

The derivative of x/(3sqrt(1+x^2)) is 1/(3(1+x^2)sqrt(1+x^2))

What is the first derivative of x/(3sqrt(1+x^2)) ?

The first derivative of x/(3sqrt(1+x^2)) is 1/(3(1+x^2)sqrt(1+x^2))

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derivative of

\frac{x}{3 1 + x ^{2}}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

What is the derivative of x/(3sqrt(1+x^2)) ?
The derivative of x/(3sqrt(1+x^2)) is 1/(3(1+x^2)sqrt(1+x^2))
What is the first derivative of x/(3sqrt(1+x^2)) ?
The first derivative of x/(3sqrt(1+x^2)) is 1/(3(1+x^2)sqrt(1+x^2))