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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{\partial}{\partial x} (4 y^{3} sin (6 x))

\frac{d y}{d x} = - x^{4} - 4 x^{3} + 5 x^{2}

\frac{d}{d x} (3 x^{2} + 8 x + 5)

\frac{\partial}{\partial y} (6 x y - 5 y)

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