Question

derive a função

f(p)= √p - p

Answer 1

Derivação.

$\mathsf{f(x) = x^{n}\,\,\,\,\,\to\,\,\,\,\,f'(x) = n \cdot x^{(n-1)}}$

Temos:

$\mathsf{f(p)=\sqrt{p}-p}\\ \\ \\ \mathsf{f(p)=p^{\frac{1}{2}}-p}$

Derivando pela regra, temos:

$\mathsf{f'(p) = \dfrac{1}{2} \cdot p^{(\frac{1}{2}-1)} - 1 \cdot p^{(1-1)}}\\ \\ \\ \mathsf{f'(p) = \dfrac{1}{2} \cdot p^{-\frac{1}{2}}-1}\\ \\ \\ \mathsf{f'(p) = \dfrac{1}{2\sqrt{p}}-1}\\ \\ \\ \boxed{\boxed{\mathsf{f'(p) = \dfrac{2\sqrt{p}}{4p}-1}}}$