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

The derivative of (xtan(x)/(x^2+1)) is (x^3sec^2(x)-x^2tan(x)+xsec^2(x)+tan(x))/((x^2+1)^2)

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

The first derivative of (xtan(x)/(x^2+1)) is (x^3sec^2(x)-x^2tan(x)+xsec^2(x)+tan(x))/((x^2+1)^2)

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

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

Solution steps

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

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

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

= \frac{( tan ( x ) + x sec ^{2} ( x ) ) ( x ^{2} + 1 ) - 2 xx tan ( x )}{( x ^{2} + 1 ) ^{2}}

Simplify

\frac{( tan ( x ) + x sec ^{2} ( x ) ) ( x ^{2} + 1 ) - 2 xx tan ( x )}{( x ^{2} + 1 ) ^{2}} : \frac{x ^{3} sec ^{2} ( x ) - x ^{2} tan ( x ) + x sec ^{2} ( x ) + tan ( x )}{( x ^{2} + 1 ) ^{2}}

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

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

y^{^{'}} + \frac{2}{x} y = \frac{1}{x ^{2}}

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

y^{^{'}} = 2 (t + 1) y, y (0) = 1

y^{^{''}} + 2 \cdot y^{^{'}} + y = e^{- t}

What is the derivative of (xtan(x)/(x^2+1)) ?
The derivative of (xtan(x)/(x^2+1)) is (x^3sec^2(x)-x^2tan(x)+xsec^2(x)+tan(x))/((x^2+1)^2)
What is the first derivative of (xtan(x)/(x^2+1)) ?
The first derivative of (xtan(x)/(x^2+1)) is (x^3sec^2(x)-x^2tan(x)+xsec^2(x)+tan(x))/((x^2+1)^2)