What is (\partial)/(\partial x)((14x)/(7x^2+y^2+6)) ?

The answer to (\partial)/(\partial x)((14x)/(7x^2+y^2+6)) is (14(-7x^2+y^2+6))/((7x^2+y^2+6)^2)

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(\partial)/(\partial x)((14x)/(7x^2+y^2+6))

\frac{\partial}{\partial x} (\frac{14 x}{7 x ^{2} + y ^{2} + 6})

\frac{14 ( - 7 x ^{2} + y ^{2} + 6 )}{( 7 x ^{2} + y ^{2} + 6 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{14 x}{7 x ^{2} + y ^{2} + 6})

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} + 6})

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} + 6 ) - \frac{\partial}{\partial x} ( 7 x ^{2} + y ^{2} + 6 ) x}{( 7 x ^{2} + y ^{2} + 6 ) ^{2}}

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

\frac{\partial}{\partial x} (7 x^{2} + y^{2} + 6) = 14 x

= 14 \cdot \frac{1 \cdot ( 7 x ^{2} + y ^{2} + 6 ) - 14 xx}{( 7 x ^{2} + y ^{2} + 6 ) ^{2}}

Simplify

14 \cdot \frac{1 \cdot ( 7 x ^{2} + y ^{2} + 6 ) - 14 xx}{( 7 x ^{2} + y ^{2} + 6 ) ^{2}} : \frac{14 ( - 7 x ^{2} + y ^{2} + 6 )}{( 7 x ^{2} + y ^{2} + 6 ) ^{2}}

= \frac{14 ( - 7 x ^{2} + y ^{2} + 6 )}{( 7 x ^{2} + y ^{2} + 6 ) ^{2}}

y = 2 x, (- 3, 3)

\int_{0}^{\frac{π}{32}} cos (8 x) d x

ln (2 - x)

n = 0 \sum \infty 6 (- \frac{1}{3})^{n}

\frac{\partial}{\partial x} (cos^{6} (x^{4} y^{5}))

What is (\partial)/(\partial x)((14x)/(7x^2+y^2+6)) ?
The answer to (\partial)/(\partial x)((14x)/(7x^2+y^2+6)) is (14(-7x^2+y^2+6))/((7x^2+y^2+6)^2)