Question

Calcule a derivada:
x√x^7

Answer 1

$\mathrm{y=x\sqrt{x^7}\ \to\ y=x.x^{\frac{7}{2}}\ \to\ y=x^{1+\frac{7}{2}}\ \to\ y=x^{\frac{9}{2}}}\\\\ \mathrm{y'=\frac{d}{dx}{[x^{\frac{9}{2}}]}\ \to\ y'=\dfrac{9}{2}(x^{\frac{9}{2}-1})\ \to\ y'=\dfrac{9}{2}x^{\frac{7}{2}}}\\\\ \mathrm{y'=\dfrac{9x^{\frac{7}{2}}}{2}\ \to\ \boxed{\mathbf{y'=\dfrac{9\sqrt{x^7}}{2}}}}$

Answer 2

$\large\boxed{\begin{array}{l}\sf f(x)=x\cdot\sqrt{x^7}\\\sf f(x)=x\cdot x^{\frac{7}{2}}\\\sf f(x)=x^{\frac{9}{2}}\\\sf f'(x)=\dfrac{9}{2}x^{\frac{7}{2}}\end{array}}$