What is (\partial)/(\partial x)(sqrt(25+18x-y)) ?

The answer to (\partial)/(\partial x)(sqrt(25+18x-y)) is 9/(sqrt(25+18x-y))

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(\partial)/(\partial x)(sqrt(25+18x-y))

\frac{\partial}{\partial x} (25 + 18 x - y)

\frac{9}{25 + 18 x - y}

Solution steps

\frac{\partial}{\partial x} (25 + 18 x - y)

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 25 + 18 x - y} \frac{\partial}{\partial x} (25 + 18 x - y)

= \frac{1}{2 25 + 18 x - y} \frac{\partial}{\partial x} (25 + 18 x - y)

\frac{\partial}{\partial x} (25 + 18 x - y) = 18

= \frac{1}{2 25 + 18 x - y} \cdot 18

Simplify

\frac{1}{2 25 + 18 x - y} \cdot 18 : \frac{9}{25 + 18 x - y}

= \frac{9}{25 + 18 x - y}

\int \frac{x}{x ^{2} + 8 x + 20} d x

\int e^{c o s (2 x)} sin (x) cos (x) d x

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

(t^{2} + x^{2}) d t + (2 t x - x) d x = 0

\frac{d}{d x} (x^{4} - 4 x^{2} - 10 x)

What is (\partial)/(\partial x)(sqrt(25+18x-y)) ?
The answer to (\partial)/(\partial x)(sqrt(25+18x-y)) is 9/(sqrt(25+18x-y))