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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int 3 cos (\frac{x}{2}) d x

\int \frac{1}{( 8 - x ) ^{2}} d x

\int x^{9} cos (x^{5}) d x

\int (4 csc (x) cot (x) + 2 sec^{2} (x)) d x

d er i v a t i v e f (x) = 20 x^{2} + 14 x - 2 x^{2}