What is (\partial)/(\partial x)(sqrt((2x-3y)^3)) ?

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

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(\partial)/(\partial x)(sqrt((2x-3y)^3))

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

3 2 x - 3 y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} ((2 x - 3 y)^{3}) = 6 (2 x - 3 y)^{2}

= \frac{1}{2 ( 2 x - 3 y ) ^{3}} \cdot 6 (2 x - 3 y)^{2}

Simplify

\frac{1}{2 ( 2 x - 3 y ) ^{3}} \cdot 6 (2 x - 3 y)^{2} : 3 2 x - 3 y

= 3 2 x - 3 y

n = 1 \sum \infty \frac{x ^{2 n}}{n !}

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

5 sin (5 t) sin (100 t)

\frac{6 t + 1}{6 t - 1}

x \to 0 lim (\frac{2 x ^{2} + 3 x}{x})

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