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Popular >

derivative of (9-x)^{1/2}

Solution

derivative of

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

Solution

- \frac{1}{2 ( 9 - x ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((9 - x)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 9 - x ) ^{\frac{1}{2}}} \frac{d}{d x} (9 - x)

= \frac{1}{2 ( 9 - x ) ^{\frac{1}{2}}} \frac{d}{d x} (9 - x)

\frac{d}{d x} (9 - x) = - 1

= \frac{1}{2 ( 9 - x ) ^{\frac{1}{2}}} (- 1)

Simplify

= - \frac{1}{2 ( 9 - x ) ^{\frac{1}{2}}}

Popular Examples

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y^{'''}-2y^{''}-4y^'+8y=0

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = 0

(\partial)/(\partial y)(-4x^3+4x)

\frac{\partial}{\partial y} (- 4 x^{3} + 4 x)

integral from 0 to pi/(28) of tan(14x)

\int_{0}^{\frac{π}{28}} tan (14 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (9-x)^{1/2} ?
The derivative of (9-x)^{1/2} is -1/(2(9-x)^{1/2)}
What is the first derivative of (9-x)^{1/2} ?
The first derivative of (9-x)^{1/2} is -1/(2(9-x)^{1/2)}