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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d}{d x} (\frac{x}{4} (1 + ln (\frac{4}{x})))

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

\int_{2}^{e^{5}} \frac{1}{x} d x

\int cos^{5} (x s i) n^{2} x d x

t an g e n t f (x) = 2 + e^{x}, at x = 1