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Popular >

derivative of 1/(6+x^2)

Solution

\frac{d}{d x} (\frac{1}{6 + x ^{2}})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{6 + x ^{2}})

Apply exponent rule:

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

= \frac{d}{d x} ((6 + x^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 6 + x ^{2} ) ^{2}} \frac{d}{d x} (6 + x^{2})

= - \frac{1}{( 6 + x ^{2} ) ^{2}} \frac{d}{d x} (6 + x^{2})

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

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

Simplify

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

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

Popular Examples

derivative of y=(e^x)/x derivative of

y = \frac{e ^{x}}{x}

tangent of f(x)=x^4-17x^2+16,\at x=2 tangent of

f (x) = x^{4} - 17 x^{2} + 16, at x = 2

area-x^2+10,-sqrt(10),-1 area

- x^{2} + 10, - 10, - 1

integral of 1/(sin^2(x)*cos^2(x))

\int \frac{1}{sin ^{2} ( x ) \cdot cos ^{2} ( x )} d x

y^{''}+6y^'+9y=(e^{-3x})/x

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{e ^{- 3 x}}{x}

Frequently Asked Questions (FAQ)

What is the derivative of 1/(6+x^2) ?
The derivative of 1/(6+x^2) is -(2x)/((6+x^2)^2)
What is the first derivative of 1/(6+x^2) ?
The first derivative of 1/(6+x^2) is -(2x)/((6+x^2)^2)