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

The answer to (\partial)/(\partial x)(sqrt(x+5y)) is 1/(2sqrt(x+5y))

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{x}{3 + x}

arcsec (2 x + 3)

\frac{d}{d x} (ln (2 x^{3} + 8 x))

\int 8^{2 x + 6} d x

\frac{8}{0.65 s + 1}

What is (\partial)/(\partial x)(sqrt(x+5y)) ?
The answer to (\partial)/(\partial x)(sqrt(x+5y)) is 1/(2sqrt(x+5y))