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derivative of 1/((1+x^2^2))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

implicit (dy)/(dx),xy=cot(xy)implicit derivative

\frac{d y}{d x}, x y = cot (x y)

(\partial)/(\partial x)(z/x ln(y)+ln(x))

\frac{\partial}{\partial x} (\frac{z}{x} ln (y) + ln (x))

integral of x/(2+sqrt(x))

\int \frac{x}{2 + x} d x

derivative of f(x)=(-x^3-x^2+x)cos(x)derivative of

f (x) = (- x^{3} - x^{2} + x) cos (x)

(dy)/(dx)=x+1/5 y

\frac{d y}{d x} = x + \frac{1}{5} y

Frequently Asked Questions (FAQ)

What is the derivative of 1/((1+x^2^2)) ?
The derivative of 1/((1+x^2^2)) is -(4x)/((1+x^2)^3)
What is the first derivative of 1/((1+x^2^2)) ?
The first derivative of 1/((1+x^2^2)) is -(4x)/((1+x^2)^3)