Question

найдите производную функции y=f(x)​

Answer 1

Ответ:

$f(x)=x^{\frac{5}{6}}\ \ ,\ \ \ f'(x)=\dfrac{5}{6}\cdot x^{-\frac{1}{6}}\\\\\\f(x)=x^{-\frac{3}{7}}\ \ ,\ \ \ f'(x)=-\dfrac{3}{7}\cdot x^{-\frac{10}{7}}$

Answer 2

$\displaystyle \star f(x)=x^n \to \ f'(x)=n\cdot x^{n-1}\star \\\\\\ 1) \ f(x)=x^{\tfrac{5}{6} } \ ; \ f'(x)=\frac{5}{6} \cdot x^{\tfrac{5}{6} -1}=\frac{5}{6} \cdot x^{-\tfrac{1}{6} } \\\\\\ 2) \ f(x)=x^{-\tfrac{3}{7} }\ ; \ f'(x)=-\frac{3}{7} \cdot x^{-\tfrac{3}{7}-1 } =-\frac{3}{7} \cdot x^{-\tfrac{10}{7} }$