d/(dθ)(4sin(θ)cos^2(θ))

Lösung

\frac{d}{d θ} (4 sin (θ) cos^{2} (θ))

4 (- 2 cos (θ) + 3 cos^{3} (θ))

Schritte zur Lösung

\frac{d}{d θ} (4 sin (θ) cos^{2} (θ))

Entferne die Konstante:

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

= 4 \frac{d}{d θ} (sin (θ) cos^{2} (θ))

Wende die Produktregel an:

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

f = sin (θ), g = cos^{2} (θ)

= 4 (\frac{d}{d θ} (sin (θ)) cos^{2} (θ) + \frac{d}{d θ} (cos^{2} (θ)) sin (θ))

\frac{d}{d θ} (sin (θ)) = cos (θ)

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

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

Vereinfache

4 (cos (θ) cos^{2} (θ) + (- sin (2 θ)) sin (θ)) : 4 (- 2 cos (θ) + 3 cos^{3} (θ))

= 4 (- 2 cos (θ) + 3 cos^{3} (θ))

a re a 3 x, 4 x^{2}

\int_{0}^{4} (\frac{1}{4 - x}) d x

\frac{\partial}{\partial y} (e^{x s i n (y)})

d er i v a t i v e arcsin (- \frac{1}{2})

\int (x^{2})^{22} d (x^{2})^{2}