(\partial)/(\partial x)(sqrt(x^2+3y^2))

Lösung

\frac{\partial}{\partial x} (x^{2} + 3 y^{2})

\frac{x}{x ^{2} + 3 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} + 3 y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 3 y^{2})

= \frac{1}{2 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (x^{2} + 3 y^{2})

\frac{\partial}{\partial x} (x^{2} + 3 y^{2}) = 2 x

= \frac{1}{2 x ^{2} + 3 y ^{2}} \cdot 2 x

Vereinfache

\frac{1}{2 x ^{2} + 3 y ^{2}} \cdot 2 x : \frac{x}{x ^{2} + 3 y ^{2}}

= \frac{x}{x ^{2} + 3 y ^{2}}

\int \frac{1}{( 36 - x ^{2} ) ^{\frac{3}{2}}} d x

d er i v a t i v e (4 t^{5} - 6 t)^{8}

\frac{\partial}{\partial x} (sin (π (x - 5 y)))

\frac{d}{d x} (cosh (x) sinh (x))

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