derivative f(x)=x^2ln(8-5x^2)

Lösung

ableitung von

f (x) = x^{2} ln (8 - 5 x^{2})

2 x ln (8 - 5 x^{2}) - \frac{10 x ^{3}}{8 - 5 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x^{2} ln (8 - 5 x^{2}))

Wende die Produktregel an:

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

f = x^{2}, g = ln (8 - 5 x^{2})

= \frac{d}{d x} (x^{2}) ln (8 - 5 x^{2}) + \frac{d}{d x} (ln (8 - 5 x^{2})) x^{2}

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

\frac{d}{d x} (ln (8 - 5 x^{2})) = - \frac{10 x}{8 - 5 x ^{2}}

= 2 x ln (8 - 5 x^{2}) + (- \frac{10 x}{8 - 5 x ^{2}}) x^{2}

Vereinfache

2 x ln (8 - 5 x^{2}) + (- \frac{10 x}{8 - 5 x ^{2}}) x^{2} : 2 x ln (8 - 5 x^{2}) - \frac{10 x ^{3}}{8 - 5 x ^{2}}

= 2 x ln (8 - 5 x^{2}) - \frac{10 x ^{3}}{8 - 5 x ^{2}}

a re a y = x^{3} - 10 x, y = 6 x

\frac{d y}{d x} = x^{6} y^{- 5}

\int_{- 5}^{5} \frac{1}{∣ x ∣ ^{\frac{2}{3}}} d x

d er i v a t i v e y = arctan (x)

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