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Beliebt Rechnen >

implicit (dy)/(dx),(cos(pix)+sin(piy))^5=23

Lösung

implizite ableitung

\frac{d y}{d x}, (cos (π x) + sin (π y))^{5} = 23

Lösung

\frac{d y}{d x} = \frac{sin ( π x )}{cos ( π y )}

Schritte zur Lösung

(cos (π x) + sin (π y))^{5} = 23

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

5 (cos (π x) + sin (π y))^{4} (- sin (π x) π + cos (π y) π \frac{d y}{d x}) = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{sin ( π x )}{cos ( π y )}

\frac{d y}{d x} = \frac{sin ( π x )}{cos ( π y )}

Beliebte Beispiele

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n = 1 \sum \infty r^{n}

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\frac{d}{d x} (x^{2} + \frac{cos ( x )}{2})

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\int e^{9} d y

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x \to - 3 lim (- 3)