derivative of sin^3(xcos(x))

Lösung

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

3 sin^{2} (x) - 4 sin^{4} (x)

Schritte zur Lösung

\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)

= \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)

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

Vereinfache

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

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

so l v e f or r, r = tan (θ) sec (θ)

f (x) = 3 x^{7}

f (x) = \frac{x ^{4}}{9}

f (x) = 12 + x

y = - 4 x + 16