derivative of ({p}(x)(10-x)ln(x+8))

Lösung

\frac{d}{d x} ((p (x)) (10 - x) ln (x + 8))

\frac{d}{d x} (p (x)) (10 - x) ln (x + 8) + (- ln (x + 8) + \frac{10 - x}{x + 8}) p (x)

Schritte zur Lösung

\frac{d}{d x} ((p (x)) (10 - x) ln (x + 8))

Wende die Produktregel an:

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

f = p (x), g = (10 - x) ln (x + 8)

= \frac{d}{d x} (p (x)) (10 - x) ln (x + 8) + \frac{d}{d x} ((10 - x) ln (x + 8)) p (x)

\frac{d}{d x} ((10 - x) ln (x + 8)) = - ln (x + 8) + \frac{10 - x}{x + 8}

= \frac{d}{d x} (p (x)) (10 - x) ln (x + 8) + (- ln (x + 8) + \frac{10 - x}{x + 8}) p (x)

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