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

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

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(\partial)/(\partial x)(2/(2x+y))

\frac{\partial}{\partial x} (\frac{2}{2 x + y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{2}{2 x + y})

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (\frac{1}{2 x + y})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{1}{( 2 x + y ) ^{2}} \cdot 2) : - \frac{4}{( 2 x + y ) ^{2}}

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

x \to - 2 lim (- x^{2} + 4 x - 6)

f (x) = x^{2} + 1, (- 2, 5)

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

x \to 0 + lim (sin (x))

\int (a x^{3} - b x^{2} - c x + d) d x

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