Question

se y=x³√x+2 então sua derivada será :

Answer 1

$y = x^3. \sqrt{x} +2 = \frac{d}{dx} (x^3.\sqrt{x} ) +\frac{d}{dx} (2)= \frac{d}{dx} (x^3.\sqrt{x} )+ 0 = \frac{d}{dx} (x^3.\sqrt{x} ) = x^3. \frac{d}{dx} \sqrt{x} + \sqrt{x} \frac{d}{dx} x^3 = x^3. \frac{d}{dx} x^{\frac{1}{2} } + \sqrt{x} \frac{d}{dx} x^3 = x^3. \frac{1}{2} x^{\frac{-1}{2} }.\sqrt{x} .3x^{2} = \frac{1}{2} . x^{\frac{5}{6} } + 3x^{\frac{5}{2} }$

Resposta: $\frac{1}{2} . x^{\frac{5}{6} } + 3x^{\frac{5}{2} }$