What is the derivative of (x^3+5/(x^2+1)) ?

The derivative of (x^3+5/(x^2+1)) is (x^4+3x^2-10x)/((x^2+1)^2)

What is the first derivative of (x^3+5/(x^2+1)) ?

The first derivative of (x^3+5/(x^2+1)) is (x^4+3x^2-10x)/((x^2+1)^2)

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\frac{d}{d x} (\frac{x ^{3} + 5}{x ^{2} + 1})

\frac{x ^{4} + 3 x ^{2} - 10 x}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} + 5}{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} + 5 ) ( x ^{2} + 1 ) - \frac{d}{d x} ( x ^{2} + 1 ) ( x ^{3} + 5 )}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (x^{3} + 5) = 3 x^{2}

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

= \frac{3 x ^{2} ( x ^{2} + 1 ) - 2 x ( x ^{3} + 5 )}{( x ^{2} + 1 ) ^{2}}

Expand

3 x^{2} (x^{2} + 1) - 2 x (x^{3} + 5) : x^{4} + 3 x^{2} - 10 x

= \frac{x ^{4} + 3 x ^{2} - 10 x}{( x ^{2} + 1 ) ^{2}}

t \to \infty lim (x)

\int_{0}^{9} π e^{- \frac{2 x}{9}} d x

\int x^{3} x^{2} + 11 d x

\frac{\partial}{\partial x} (\frac{( x y )}{x - y})

\int_{\frac{1}{2}}^{5} 14 x ln (2 x) d x

What is the derivative of (x^3+5/(x^2+1)) ?
The derivative of (x^3+5/(x^2+1)) is (x^4+3x^2-10x)/((x^2+1)^2)
What is the first derivative of (x^3+5/(x^2+1)) ?
The first derivative of (x^3+5/(x^2+1)) is (x^4+3x^2-10x)/((x^2+1)^2)