What is (\partial)/(\partial x)(sqrt(6x-2y)) ?

The answer to (\partial)/(\partial x)(sqrt(6x-2y)) is 3/(sqrt(6x-2y))

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(\partial)/(\partial x)(sqrt(6x-2y))

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

\frac{3}{6 x - 2 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 6 x - 2 y} \frac{\partial}{\partial x} (6 x - 2 y)

= \frac{1}{2 6 x - 2 y} \frac{\partial}{\partial x} (6 x - 2 y)

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

= \frac{1}{2 6 x - 2 y} \cdot 6

Simplify

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

= \frac{3}{6 x - 2 y}

y^{^{'}} = 4 x + y, y (0) = 7

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = 1

\frac{2}{5 x + 3}

\int \frac{csc ^{2} ( x )}{cot ^{3} ( x )} d x

ln (4 x^{5} + 1)

What is (\partial)/(\partial x)(sqrt(6x-2y)) ?
The answer to (\partial)/(\partial x)(sqrt(6x-2y)) is 3/(sqrt(6x-2y))