What is (\partial)/(\partial x)(sqrt(5x+y)) ?

The answer to (\partial)/(\partial x)(sqrt(5x+y)) is 5/(2sqrt(5x+y))

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(\partial)/(\partial x)(sqrt(5x+y))

\frac{\partial}{\partial x} (5 x + y)

\frac{5}{2 5 x + y}

Solution steps

\frac{\partial}{\partial x} (5 x + y)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 5 x + y} \frac{\partial}{\partial x} (5 x + y)

= \frac{1}{2 5 x + y} \frac{\partial}{\partial x} (5 x + y)

\frac{\partial}{\partial x} (5 x + y) = 5

= \frac{1}{2 5 x + y} \cdot 5

Simplify

\frac{1}{2 5 x + y} \cdot 5 : \frac{5}{2 5 x + y}

= \frac{5}{2 5 x + y}

x \to - 1 lim (\frac{x}{x ^{2} + x})

f (x) = e^{x^{2} - 6}

x \to 0 lim (x \cdot (ln (x))^{2})

\frac{\partial}{\partial x} (2 sin (2 x) cos (2 y))

\frac{\partial}{\partial x} (\frac{1}{x + 1})

What is (\partial)/(\partial x)(sqrt(5x+y)) ?
The answer to (\partial)/(\partial x)(sqrt(5x+y)) is 5/(2sqrt(5x+y))