derivative 2xsin(x)+cos(x)x^2

Lösung

ableitung von

2 x sin (x) + cos (x) x^{2}

- x^{2} sin (x) + 4 x cos (x) + 2 sin (x)

Schritte zur Lösung

\frac{d}{d x} (2 x sin (x) + cos (x) x^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (2 x sin (x)) = 2 (sin (x) + x cos (x))

\frac{d}{d x} (cos (x) x^{2}) = - x^{2} sin (x) + 2 x cos (x)

= 2 (sin (x) + x cos (x)) - x^{2} sin (x) + 2 x cos (x)

Vereinfache

2 (sin (x) + x cos (x)) - x^{2} sin (x) + 2 x cos (x) : - x^{2} sin (x) + 4 x cos (x) + 2 sin (x)

= - x^{2} sin (x) + 4 x cos (x) + 2 sin (x)

\int 4 e^{- 4 x} d x

\int_{0}^{\frac{5 π}{4}} 3 tan (\frac{x}{5}) d x

im pl i c i t \frac{d y}{d x}, y = 7^{x}

d er i v a t i v e y = \frac{0.9 e ^{x}}{tan ( x )}

f (x) = - 4 sin (2 x) + 3 cos (3 x)