(\partial)/(\partial x)(sqrt(x^2+y^2-5))

Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

\frac{x}{x ^{2} + y ^{2} - 5}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + y ^{2} - 5} \frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

= \frac{1}{2 x ^{2} + y ^{2} - 5} \frac{\partial}{\partial x} (x^{2} + y^{2} - 5)

\frac{\partial}{\partial x} (x^{2} + y^{2} - 5) = 2 x

= \frac{1}{2 x ^{2} + y ^{2} - 5} \cdot 2 x

Vereinfache

\frac{1}{2 x ^{2} + y ^{2} - 5} \cdot 2 x : \frac{x}{x ^{2} + y ^{2} - 5}

= \frac{x}{x ^{2} + y ^{2} - 5}

t an g e n t f (x) = x^{3} - x, at x = 1

\int \frac{1}{5 + 4 x - x ^{2}} d x

x \to - \infty lim (\frac{( 4 x ^{2} + 1 )}{( 2 - 7 x )})

x y^{^{'}} + 4 y = - 25 x sin (x^{5})

\frac{d}{d x} (\frac{3}{7 x ^{4} - 5 x ^{2} + 1})