d/(dθ)(4sin^2(θ)cos(θ))

Lösung

\frac{d}{d θ} (4 sin^{2} (θ) cos (θ))

4 (sin (2 θ) cos (θ) - sin^{3} (θ))

Schritte zur Lösung

\frac{d}{d θ} (4 sin^{2} (θ) cos (θ))

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = sin^{2} (θ), g = cos (θ)

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

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

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

Vereinfache

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

= 4 (sin (2 θ) cos (θ) - sin^{3} (θ))

\frac{d}{d x} (\frac{9 ( 1 - sin ( x ) )}{2 cos ( x )})

\frac{d}{d y} (y^{2})

\int \frac{1}{( x ln ( x ) )} d x

\int \frac{8 + 3 x}{x ( x ^{2} + 4 )} d x

d er i v a t i v e x^{3} - 15 x^{2} + 72 x