(\partial)/(\partial x)(sqrt(5x^2+3y^2))

Lösung

\frac{\partial}{\partial x} (5 x^{2} + 3 y^{2})

\frac{5 x}{5 x ^{2} + 3 y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (5 x^{2} + 3 y^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 5 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (5 x^{2} + 3 y^{2})

= \frac{1}{2 5 x ^{2} + 3 y ^{2}} \frac{\partial}{\partial x} (5 x^{2} + 3 y^{2})

\frac{\partial}{\partial x} (5 x^{2} + 3 y^{2}) = 10 x

= \frac{1}{2 5 x ^{2} + 3 y ^{2}} \cdot 10 x

Vereinfache

\frac{1}{2 5 x ^{2} + 3 y ^{2}} \cdot 10 x : \frac{5 x}{5 x ^{2} + 3 y ^{2}}

= \frac{5 x}{5 x ^{2} + 3 y ^{2}}

d er i v a t i v e f (x) = \frac{3 t}{t - 6}

\int \frac{y}{( 1 + y ^{2} ) ^{\frac{1}{2}}} d y

\int (x sin (x^{2})) d x

\int_{1}^{4} \frac{3}{t ^{4}} d t

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = 3, y^{^{'}} (0) = 0