derivative of 4sin^3(xcos(x))

Lösung

\frac{d}{d x} (4 sin^{3} (x) cos (x))

12 sin^{2} (x) - 16 sin^{4} (x)

Schritte zur Lösung

\frac{d}{d x} (4 sin^{3} (x) cos (x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (sin^{3} (x) cos (x))

Wende die Produktregel an:

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

f = sin^{3} (x), g = cos (x)

= 4 (\frac{d}{d x} (sin^{3} (x)) cos (x) + \frac{d}{d x} (cos (x)) sin^{3} (x))

\frac{d}{d x} (sin^{3} (x)) = 3 sin^{2} (x) cos (x)

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

= 4 (3 sin^{2} (x) cos (x) cos (x) + (- sin (x)) sin^{3} (x))

Vereinfache

4 (3 sin^{2} (x) cos (x) cos (x) + (- sin (x)) sin^{3} (x)) : 12 sin^{2} (x) - 16 sin^{4} (x)

= 12 sin^{2} (x) - 16 sin^{4} (x)

\int \frac{e ^{x}}{3 + e ^{x}} d x

H (- 5) = 2^{x}

\int (5 x + 3) d x

\int (2 x - 1) e^{- x} d x

y^{^{'}} - t^{2} y = 0