What is the derivative of (2x+5x^{-2/5}/(x^2+1)) ?

The derivative of (2x+5x^{-2/5}/(x^2+1)) is (-12x^2-2x^{17/5}-2+2x^{7/5})/(x^{7/5)(x^2+1)^2}

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

The first derivative of (2x+5x^{-2/5}/(x^2+1)) is (-12x^2-2x^{17/5}-2+2x^{7/5})/(x^{7/5)(x^2+1)^2}

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

\frac{- 12 x ^{2} - 2 x ^{\frac{17}{5}} - 2 + 2 x ^{\frac{7}{5}}}{x ^{\frac{7}{5}} ( x ^{2} + 1 ) ^{2}}

Solution steps

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

\frac{d}{d x} (2 x + 5 x^{- \frac{2}{5}}) = 2 - \frac{2}{x ^{\frac{7}{5}}}

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

= \frac{( 2 - \frac{2}{x ^{\frac{7}{5}}} ) ( x ^{2} + 1 ) - 2 x ( 2 x + 5 x ^{- \frac{2}{5}} )}{( x ^{2} + 1 ) ^{2}}

Simplify

\frac{( 2 - \frac{2}{x ^{\frac{7}{5}}} ) ( x ^{2} + 1 ) - 2 x ( 2 x + 5 x ^{- \frac{2}{5}} )}{( x ^{2} + 1 ) ^{2}} : \frac{- 12 x ^{2} - 2 x ^{\frac{17}{5}} - 2 + 2 x ^{\frac{7}{5}}}{x ^{\frac{7}{5}} ( x ^{2} + 1 ) ^{2}}

= \frac{- 12 x ^{2} - 2 x ^{\frac{17}{5}} - 2 + 2 x ^{\frac{7}{5}}}{x ^{\frac{7}{5}} ( x ^{2} + 1 ) ^{2}}

\frac{\partial}{\partial x} (x^{4} y^{3} - 4 x^{2} y + y^{5})

f (x) = cos (\frac{π x}{2}), at x = 0.8

f (x) = 2 x^{4} e^{x}

\int \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x + C d x

\int \frac{1}{200 + 3 t} d t

What is the derivative of (2x+5x^{-2/5}/(x^2+1)) ?
The derivative of (2x+5x^{-2/5}/(x^2+1)) is (-12x^2-2x^{17/5}-2+2x^{7/5})/(x^{7/5)(x^2+1)^2}
What is the first derivative of (2x+5x^{-2/5}/(x^2+1)) ?
The first derivative of (2x+5x^{-2/5}/(x^2+1)) is (-12x^2-2x^{17/5}-2+2x^{7/5})/(x^{7/5)(x^2+1)^2}