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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = x^{3}, (- 1, 2)

\frac{\partial}{\partial x} (3 + x ln (x y - 9))

y^{^{''}} + 3 y^{^{'}} + 3.25 y = 3 cos (t) - 1.5 sin (t)

y^{^{'}} = \frac{e ^{x + y}}{1 + e ^{x}}

y = \frac{29}{x ^{3}}, [1, 10]

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