Question

Derivada f(x)= $-3x^{-8}$+$2 \sqrt{x}}$

Answer 1

Olá


Formulário:

Derivada de polinômios:

y = xⁿ
y' = n.xⁿ⁻¹

Propriedades (Potencia/radiciação)

$\displaystyle\mathsf{ \sqrt[n]{a^m}~=~a^{ \frac{m}{n} } }\\\\\\\mathsf{a^{-b}~=~ \frac{1}{a^b} }$



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$\displaystyle \mathsf{f(x)~=~-3x^{-8}+2 \sqrt{x} }\\\\\\\mathsf{f(x)~=~-3x^{-8}+2 x^{ \frac{1}{2} }}\\\\\\\mathsf{f'(x)~=~(-8)\cdot(-3)x^{-8-1}+ \frac{1}{\diagup\!\!\!\!2}\cdot \diagup\!\!\!\!2 x^{ \frac{1}{2}-1 }}\\\\\\\boxed{\mathsf{f'(x)~=~24x^{-9}+ x^{ -\frac{1}{2} }}}$


Ou se preferir dar a resposta como raiz.


$\displaystyle \boxed{\mathsf{f'(x)~=~24x^{-9}+ \frac{1}{ \sqrt{x} } }}}}$