Question

$x \sqrt{x } find \: derivative \: by \\ \: first \: principle$
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Answer 1

Answer:

Step-by-step explanation:

A derivative is simply a measure of the rate of change. It can be the rate of change of distance with respect to time or the temperature with respect to distance. We want to measure the rate of change of a function y = f ( x ) y = f(x) y=f(x) with respect to its variable x x x.

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Answer 2

Answer:

The derivative is $\frac{3}{2}x^{\frac{1}{2}}$.

Step-by-step explanation:

The expression is, $x\sqrt{x}$.

Simplify the expression as follows:

$x\sqrt{x}=x\times x^{\frac{1}{2}}=x^{1+\frac{1}{2}}=x^{\frac{3}{2}}$

Compute the derivative of $x^{\frac{3}{2}}$ as follows:

$\frac{d}{dx}(x^{\frac{3}{2}})=\frac{3}{2}\times (x^{\frac{3}{2}-1})=\frac{3}{2}\times (x^{\frac{1}{2}})=\frac{3}{2}x^{\frac{1}{2}}$

Thus, the derivative is $\frac{3}{2}x^{\frac{1}{2}}$.