(\partial)/(\partial h)(pi/3 h^2(3r-h))

Lösung

\frac{\partial}{\partial h} (\frac{π}{3} h^{2} (3 r - h))

πh (2 r - h)

Schritte zur Lösung

\frac{\partial}{\partial h} (\frac{π}{3} h^{2} (3 r - h))

Behandle

r

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{π}{3} \frac{\partial}{\partial h} (h^{2} (3 r - h))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = h^{2}, g = 3 r - h

= \frac{π}{3} (\frac{\partial}{\partial h} (h^{2}) (3 r - h) + \frac{\partial}{\partial h} (3 r - h) h^{2})

\frac{\partial}{\partial h} (h^{2}) = 2 h

\frac{\partial}{\partial h} (3 r - h) = - 1

= \frac{π}{3} (2 h (3 r - h) + (- 1) h^{2})

Vereinfache

\frac{π}{3} (2 h (3 r - h) + (- 1) h^{2}) : πh (2 r - h)

= πh (2 r - h)

\frac{d}{d x} (cos (x - 7 x^{2}))

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