derivative of ({r}(x(x)^2-x^2)^{1/2})

Lösung

\frac{d}{d x} ((r (x) (x)^{2} - x^{2})^{\frac{1}{2}})

\frac{x \frac{d}{d x} ( r ( x ) ) + 2 r ( x ) - 2}{2 ( r ( x ) - 1 ) ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{d}{d x} ((r (x) (x)^{2} - x^{2})^{\frac{1}{2}})

Wende die Kettenregel an:

\frac{1}{2 ( r ( x ) x ^{2} - x ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (r (x) x^{2} - x^{2})

= \frac{1}{2 ( r ( x ) x ^{2} - x ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (r (x) x^{2} - x^{2})

\frac{d}{d x} (r (x) x^{2} - x^{2}) = \frac{d}{d x} (r (x)) x^{2} + 2 x r (x) - 2 x

= \frac{1}{2 ( r ( x ) x ^{2} - x ^{2} ) ^{\frac{1}{2}}} (\frac{d}{d x} (r (x)) x^{2} + 2 x r (x) - 2 x)

Vereinfache

\frac{1}{2 ( r ( x ) x ^{2} - x ^{2} ) ^{\frac{1}{2}}} (\frac{d}{d x} (r (x)) x^{2} + 2 x r (x) - 2 x) : \frac{x \frac{d}{d x} ( r ( x ) ) + 2 r ( x ) - 2}{2 ( r ( x ) - 1 ) ^{\frac{1}{2}}}

= \frac{x \frac{d}{d x} ( r ( x ) ) + 2 r ( x ) - 2}{2 ( r ( x ) - 1 ) ^{\frac{1}{2}}}

t an g e n t f (x) = sin (3 x), (\frac{π}{18}, \frac{2}{2})

\frac{d}{d x} (sin^{2} (b x) + x^{2} + 1)

\int \frac{3 x - 6}{x ^{2} - 4 x + 5} d x

\frac{\partial}{\partial x} (x z x + y)

\int - 5 x^{4} e^{x^{5}} d x