derivative of 4(x^2+5x+2tan(-x))

Lösung

\frac{d}{d x} (4 (x^{2} + 5 x + 2) tan (- x))

- 4 (sec^{2} (x) (2 + x^{2} + 5 x) + (2 x + 5) tan (x))

Schritte zur Lösung

\frac{d}{d x} (4 (x^{2} + 5 x + 2) tan (- x))

Vereinfache

4 (x^{2} + 5 x + 2) tan (- x) : - 4 tan (x) (2 + x^{2} + 5 x)

= \frac{d}{d x} (- 4 tan (x) (2 + x^{2} + 5 x))

Entferne die Konstante:

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

= - 4 \frac{d}{d x} (tan (x) (2 + x^{2} + 5 x))

Wende die Produktregel an:

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

f = tan (x), g = 2 + x^{2} + 5 x

= - 4 (\frac{d}{d x} (tan (x)) (2 + x^{2} + 5 x) + \frac{d}{d x} (2 + x^{2} + 5 x) tan (x))

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

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

= - 4 (sec^{2} (x) (2 + x^{2} + 5 x) + (2 x + 5) tan (x))

\frac{\partial}{\partial x} (2 x^{0.5} + y)

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d er i v a t i v e f (x) = 8 x e^{x} csc (x)

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