derivative 4x^2tan(x)

Lösung

ableitung von

4 x^{2} tan (x)

4 (2 x tan (x) + sec^{2} (x) x^{2})

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} tan (x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{2} tan (x))

Wende die Produktregel an:

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

f = x^{2}, g = tan (x)

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

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

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

= 4 (2 x tan (x) + sec^{2} (x) x^{2})

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