What is (\partial)/(\partial x)(2/(8x+3y)) ?

The answer to (\partial)/(\partial x)(2/(8x+3y)) is -(16)/((8x+3y)^2)

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(\partial)/(\partial x)(2/(8x+3y))

\frac{\partial}{\partial x} (\frac{2}{8 x + 3 y})

- \frac{16}{( 8 x + 3 y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{2}{8 x + 3 y})

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (\frac{1}{8 x + 3 y})

Apply exponent rule:

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

= 2 \frac{\partial}{\partial x} ((8 x + 3 y)^{- 1})

Apply the chain rule:

- \frac{1}{( 8 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (8 x + 3 y)

= - \frac{1}{( 8 x + 3 y ) ^{2}} \frac{\partial}{\partial x} (8 x + 3 y)

\frac{\partial}{\partial x} (8 x + 3 y) = 8

= 2 (- \frac{1}{( 8 x + 3 y ) ^{2}} \cdot 8)

Simplify

2 (- \frac{1}{( 8 x + 3 y ) ^{2}} \cdot 8) : - \frac{16}{( 8 x + 3 y ) ^{2}}

= - \frac{16}{( 8 x + 3 y ) ^{2}}

\frac{d}{d x} (- 12 x - 6)

\int \frac{1}{x} - \frac{1}{e ^{2 x}} d x

x \to 0 - lim (x^{2} csc (x))

\frac{3 - x ^{2}}{8 + x ^{2}}

What is (\partial)/(\partial x)(2/(8x+3y)) ?
The answer to (\partial)/(\partial x)(2/(8x+3y)) is -(16)/((8x+3y)^2)