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Derivative of 1/radical x

User Robyflc
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1 Answer

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The derivative of
\( (1)/(√(x)) \) with respect to
\( x \) is
\( -(1)/(2√(x^3)) \).

How did we get the value?

To find the derivative of
\( (1)/(√(x)) \) , you can use the rules of differentiation.

Let \( y =
(1)/(√(x)) \). To find
\( (dy)/(dx) \):


\[ y = x^(-1/2) \]

Now, apply the power rule for differentiation, which states that if
\( y = x^n \), then
\( (dy)/(dx) = nx^(n-1) \):


\[ (dy)/(dx) = -(1)/(2)x^(-3/2) \]

Now, you can simplify the expression:


\[ (dy)/(dx) = -(1)/(2√(x^3)) \]

So, the derivative of
\( (1)/(√(x)) \) with respect to
\( x \) is
\( -(1)/(2√(x^3)) \).

User Alaric
by
8.8k points

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