What is (\partial)/(\partial x)(1/(4-3x)) ?

The answer to (\partial)/(\partial x)(1/(4-3x)) is 3/((4-3x)^2)

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(\partial)/(\partial x)(1/(4-3x))

\frac{\partial}{\partial x} (\frac{1}{4 - 3 x})

\frac{3}{( 4 - 3 x ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{4 - 3 x})

Apply exponent rule:

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

= \frac{\partial}{\partial x} ((4 - 3 x)^{- 1})

Apply the chain rule:

- \frac{1}{( 4 - 3 x ) ^{2}} \frac{\partial}{\partial x} (4 - 3 x)

= - \frac{1}{( 4 - 3 x ) ^{2}} \frac{\partial}{\partial x} (4 - 3 x)

\frac{\partial}{\partial x} (4 - 3 x) = - 3

= - \frac{1}{( 4 - 3 x ) ^{2}} (- 3)

Simplify

- \frac{1}{( 4 - 3 x ) ^{2}} (- 3) : \frac{3}{( 4 - 3 x ) ^{2}}

= \frac{3}{( 4 - 3 x ) ^{2}}

What is (\partial)/(\partial x)(1/(4-3x)) ?
The answer to (\partial)/(\partial x)(1/(4-3x)) is 3/((4-3x)^2)