What is the derivative of $x^{\frac{2}{3}}$ $x^(2/3)$ ?

Question

9307 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-04T13:36:54

This is a simply appliance of power rule, which states

Be $y = a^{n}$ $y=a^n$ , then $\frac{d y}{d x} = n \cdot a^{n - 1}$ $(dy)/(dx)=n*a^(n-1)$

Thus,

$\frac{d y}{d x} = x^{\frac{3}{2} - 1} = x^{\frac{1}{2}} = \sqrt{x}$ $(dy)/(dx)=x^(3/2-1)=x^(1/2)=sqrt(x)$

What is the derivative of x23x^(2/3)?