What is (\partial)/(\partial x)((5x)/(4x^2+1)) ?

The answer to (\partial)/(\partial x)((5x)/(4x^2+1)) is (5(-4x^2+1))/((4x^2+1)^2)

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(\partial)/(\partial x)((5x)/(4x^2+1))

\frac{\partial}{\partial x} (\frac{5 x}{4 x ^{2} + 1})

\frac{5 ( - 4 x ^{2} + 1 )}{( 4 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{5 x}{4 x ^{2} + 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial x} (\frac{x}{4 x ^{2} + 1})

Apply the Quotient Rule:

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

= 5 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( 4 x ^{2} + 1 ) - \frac{\partial}{\partial x} ( 4 x ^{2} + 1 ) x}{( 4 x ^{2} + 1 ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (4 x^{2} + 1) = 8 x

= 5 \cdot \frac{1 \cdot ( 4 x ^{2} + 1 ) - 8 xx}{( 4 x ^{2} + 1 ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot ( 4 x ^{2} + 1 ) - 8 xx}{( 4 x ^{2} + 1 ) ^{2}} : \frac{5 ( - 4 x ^{2} + 1 )}{( 4 x ^{2} + 1 ) ^{2}}

= \frac{5 ( - 4 x ^{2} + 1 )}{( 4 x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (\frac{e ^{x^{2}}}{x ^{2}})

7 x - x^{2}

\int e^{x} 35 + e^{x} d x

\int \frac{6}{x ^{2} + 1} - x^{2} d x

\frac{\partial}{\partial x} (ln (1 + \frac{1}{x}))

What is (\partial)/(\partial x)((5x)/(4x^2+1)) ?
The answer to (\partial)/(\partial x)((5x)/(4x^2+1)) is (5(-4x^2+1))/((4x^2+1)^2)