Решебник по алгебре 11 класс Никольский Параграф 4. Производная Задание 71

\[\boxed{\mathbf{71}\mathbf{.}}\]

\[\textbf{а)}\ y = \sqrt{x};\ \ x > 0;\ \ x = y^{2};\ \ \]

\[y > 0\]

\[x^{'}(y) = 2y;\]

\[f^{'}(x) = \frac{1}{(2y)^{'}} = \frac{1}{2\sqrt{x}}.\]

\[\textbf{б)}\ y = - \sqrt{x};\ \ x > 0;\ \ x = y^{2};\]

\[\ \ y < 0\]

\[x^{'}(y) = 2y;\]

\[f^{'}(x) = \frac{1}{(2y)^{'}} = - \frac{1}{2\sqrt{x}}.\]

\[\textbf{в)}\ y = \ln x;\ \ x > 0;\ \ x = e^{y};\ \]

\[\ y \in R\]

\[x^{'}(y) = e^{y};\]

\[f^{'}(x) = \frac{1}{e^{y}} = \frac{1}{x}.\]