What is the derivative of f(x)=(2-x^2)/(3+x^2) ?

The derivative of f(x)=(2-x^2)/(3+x^2) is -(10x)/((3+x^2)^2)

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

The first derivative of f(x)=(2-x^2)/(3+x^2) is -(10x)/((3+x^2)^2)

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derivative of

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

- \frac{10 x}{( 3 + x ^{2} ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 2 x ) ( 3 + x ^{2} ) - 2 x ( 2 - x ^{2} )}{( 3 + x ^{2} ) ^{2}} : - \frac{10 x}{( 3 + x ^{2} ) ^{2}}

= - \frac{10 x}{( 3 + x ^{2} ) ^{2}}

n = 1 \sum \infty arctan (18 n)

n = 0 \sum \infty (1.1)^{n}

y = arctan (x^{2} + 1)

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

x \to 5 lim (\frac{x - 25}{x - 5})

What is the derivative of f(x)=(2-x^2)/(3+x^2) ?
The derivative of f(x)=(2-x^2)/(3+x^2) is -(10x)/((3+x^2)^2)
What is the first derivative of f(x)=(2-x^2)/(3+x^2) ?
The first derivative of f(x)=(2-x^2)/(3+x^2) is -(10x)/((3+x^2)^2)