What is (\partial)/(\partial x)((1-x-4y)^{1/2}) ?

The answer to (\partial)/(\partial x)((1-x-4y)^{1/2}) is -1/(2(1-x-4y)^{1/2)}

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(\partial)/(\partial x)((1-x-4y)^{1/2})

\frac{\partial}{\partial x} ((1 - x - 4 y)^{\frac{1}{2}})

- \frac{1}{2 ( 1 - x - 4 y ) ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} ((1 - x - 4 y)^{\frac{1}{2}})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 ( 1 - x - 4 y ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (1 - x - 4 y)

= \frac{1}{2 ( 1 - x - 4 y ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (1 - x - 4 y)

\frac{\partial}{\partial x} (1 - x - 4 y) = - 1

= \frac{1}{2 ( 1 - x - 4 y ) ^{\frac{1}{2}}} (- 1)

Simplify

= - \frac{1}{2 ( 1 - x - 4 y ) ^{\frac{1}{2}}}

\frac{\partial}{\partial x} (5 e^{x^{5} y})

f (x) = \frac{x ^{2} + 2 x + 1}{x ^{2} - 2 x + 1}

\int 7 sin (5 x) sin (x) d x

x \to 0 lim (4 x - ∣ x ∣)

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

What is (\partial)/(\partial x)((1-x-4y)^{1/2}) ?
The answer to (\partial)/(\partial x)((1-x-4y)^{1/2}) is -1/(2(1-x-4y)^{1/2)}