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

The derivative of (x^3+3x/(x^2+1)) is (x^4+3)/((x^2+1)^2)

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

The first derivative of (x^3+3x/(x^2+1)) is (x^4+3)/((x^2+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

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

x y^{^{'}} + 4 y = x^{3} - x

\int t \cdot e^{- t} d t

(y + y cos (x y)) d x + (x + x cos (x y)) d y = 0

\int_{1}^{e} ln (9 x) d x

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