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Popular >

derivative of (8x^2-5)^{1/2}

Solution

derivative of

(8 x^{2} - 5)^{\frac{1}{2}}

Solution

\frac{8 x}{( 8 x ^{2} - 5 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((8 x^{2} - 5)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x^{2} - 5)

= \frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \frac{d}{d x} (8 x^{2} - 5)

\frac{d}{d x} (8 x^{2} - 5) = 16 x

= \frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \cdot 16 x

Simplify

\frac{1}{2 ( 8 x ^{2} - 5 ) ^{\frac{1}{2}}} \cdot 16 x : \frac{8 x}{( 8 x ^{2} - 5 ) ^{\frac{1}{2}}}

= \frac{8 x}{( 8 x ^{2} - 5 ) ^{\frac{1}{2}}}

Popular Examples

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\int_{0}^{3} (2 x - 1) d x

(\partial)/(\partial z)(x^2+(y-1)^2+z^2)

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

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\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{4})

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x \to 2 - lim (\frac{m x - 3 m}{x - 3})

Frequently Asked Questions (FAQ)

What is the derivative of (8x^2-5)^{1/2} ?
The derivative of (8x^2-5)^{1/2} is (8x)/((8x^2-5)^{1/2)}
What is the first derivative of (8x^2-5)^{1/2} ?
The first derivative of (8x^2-5)^{1/2} is (8x)/((8x^2-5)^{1/2)}