What is (\partial)/(\partial x)((14x)/(7x^2+y^2+2)) ?

The answer to (\partial)/(\partial x)((14x)/(7x^2+y^2+2)) is (14(-7x^2+y^2+2))/((7x^2+y^2+2)^2)

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(\partial)/(\partial x)((14x)/(7x^2+y^2+2))

\frac{\partial}{\partial x} (\frac{14 x}{7 x ^{2} + y ^{2} + 2})

\frac{14 ( - 7 x ^{2} + y ^{2} + 2 )}{( 7 x ^{2} + y ^{2} + 2 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{14 x}{7 x ^{2} + y ^{2} + 2})

Treat

y

as a constant

Take the constant out:

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

= 14 \frac{\partial}{\partial x} (\frac{x}{7 x ^{2} + y ^{2} + 2})

Apply the Quotient Rule:

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

= 14 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( 7 x ^{2} + y ^{2} + 2 ) - \frac{\partial}{\partial x} ( 7 x ^{2} + y ^{2} + 2 ) x}{( 7 x ^{2} + y ^{2} + 2 ) ^{2}}

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

\frac{\partial}{\partial x} (7 x^{2} + y^{2} + 2) = 14 x

= 14 \cdot \frac{1 \cdot ( 7 x ^{2} + y ^{2} + 2 ) - 14 xx}{( 7 x ^{2} + y ^{2} + 2 ) ^{2}}

Simplify

14 \cdot \frac{1 \cdot ( 7 x ^{2} + y ^{2} + 2 ) - 14 xx}{( 7 x ^{2} + y ^{2} + 2 ) ^{2}} : \frac{14 ( - 7 x ^{2} + y ^{2} + 2 )}{( 7 x ^{2} + y ^{2} + 2 ) ^{2}}

= \frac{14 ( - 7 x ^{2} + y ^{2} + 2 )}{( 7 x ^{2} + y ^{2} + 2 ) ^{2}}

\int_{0}^{1} \frac{1}{x + 2} d x

\frac{7 s + 4}{2 s ^{2} + 16 s + 30}

\frac{x - 2}{x ^{2} - 4}

x \to 2 lim (- x + 2 x^{2} - 1)

\frac{10}{s ^{2} + 2 s + 10}

What is (\partial)/(\partial x)((14x)/(7x^2+y^2+2)) ?
The answer to (\partial)/(\partial x)((14x)/(7x^2+y^2+2)) is (14(-7x^2+y^2+2))/((7x^2+y^2+2)^2)