What is (\partial)/(\partial x)(A/(x+sqrt(5)x)) ?

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

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(\partial)/(\partial x)(A/(x+sqrt(5)x))

\frac{\partial}{\partial x} (\frac{A}{x + 5 x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{A}{x + 5 x})

Take the constant out:

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

= A \frac{\partial}{\partial x} (\frac{1}{x + 5 x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= A \frac{\partial}{\partial x} ((x + 5 x)^{- 1})

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} ((1 + x) (x^{3}))

\frac{\partial}{\partial y} (x^{\frac{1}{3}} y^{\frac{2}{3}})

\int \frac{x ^{2} + 6 x + 2}{x ^{3} + 9 x ^{2} + 6 x + 9} d x

y^{^{'}} + 0.06 y = 6

n = 1 \sum \infty \frac{( n ! )}{n ^{n}}

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