What is the derivative of y= 1/(x^2+x^2) ?

The derivative of y= 1/(x^2+x^2) is -1/(x^3)

What is the first derivative of y= 1/(x^2+x^2) ?

The first derivative of y= 1/(x^2+x^2) is -1/(x^3)

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derivative of

y = \frac{1}{x ^{2} + x ^{2}}

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{2} + x^{2}) = 4 x

= - \frac{1}{( x ^{2} + x ^{2} ) ^{2}} \cdot 4 x

Simplify

- \frac{1}{( x ^{2} + x ^{2} ) ^{2}} \cdot 4 x : - \frac{1}{x ^{3}}

= - \frac{1}{x ^{3}}

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