What is (\partial)/(\partial x)((2x)/(9-tan(x))) ?

The answer to (\partial)/(\partial x)((2x)/(9-tan(x))) is (2(9-tan(x)+xsec^2(x)))/((9-tan(x))^2)

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(\partial)/(\partial x)((2x)/(9-tan(x)))

\frac{\partial}{\partial x} (\frac{2 x}{9 - tan ( x )})

\frac{2 ( 9 - tan ( x ) + x sec ^{2} ( x ) )}{( 9 - tan ( x ) ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{2 x}{9 - tan ( x )})

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (\frac{x}{9 - tan ( x )})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( 9 - tan ( x ) ) - \frac{\partial}{\partial x} ( 9 - tan ( x ) ) x}{( 9 - tan ( x ) ) ^{2}}

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

\frac{\partial}{\partial x} (9 - tan (x)) = - sec^{2} (x)

= 2 \cdot \frac{1 \cdot ( 9 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 9 - tan ( x ) ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 9 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 9 - tan ( x ) ) ^{2}} : \frac{2 ( 9 - tan ( x ) + x sec ^{2} ( x ) )}{( 9 - tan ( x ) ) ^{2}}

= \frac{2 ( 9 - tan ( x ) + x sec ^{2} ( x ) )}{( 9 - tan ( x ) ) ^{2}}

\int \frac{x ^{11}}{2 x ^{6} + 2} d x

y^{^{''}} + y^{^{'}} - 6 y = 2 x

t^{2} y^{^{'}} + t y = y

n = 1 \sum \infty \frac{3}{n ^{2} + 3 n}

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

What is (\partial)/(\partial x)((2x)/(9-tan(x))) ?
The answer to (\partial)/(\partial x)((2x)/(9-tan(x))) is (2(9-tan(x)+xsec^2(x)))/((9-tan(x))^2)