derivative of 4-sqrt(x^2+y^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4) - \frac{d}{d x} (x^{2} + y^{2})

\frac{d}{d x} (4) = 0

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

= 0 - \frac{x + y \frac{d y}{d x}}{x ^{2} + y ^{2}}

Vereinfache

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

\int (\frac{12 x ^{4} + 3 x ^{2} + 6 a x}{2 x}) d x

x \to 3 + lim (\frac{7}{x - 3})

\int \frac{2 x + 4}{x ^{2}} d x

n = 0 \sum \infty \frac{1}{( 2 ^{n} )}

P - P^{2} = \frac{d P}{d t}