derivative of (sin^5(x)/5-(sin^7(x))/7)

Lösung

\frac{d}{d x} (\frac{sin ^{5} ( x )}{5} - \frac{sin ^{7} ( x )}{7})

sin^{4} (x) cos^{3} (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ^{5} ( x )}{5} - \frac{sin ^{7} ( x )}{7})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{sin ^{5} ( x )}{5}) - \frac{d}{d x} (\frac{sin ^{7} ( x )}{7})

\frac{d}{d x} (\frac{sin ^{5} ( x )}{5}) = sin^{4} (x) cos (x)

\frac{d}{d x} (\frac{sin ^{7} ( x )}{7}) = sin^{6} (x) cos (x)

= sin^{4} (x) cos (x) - sin^{6} (x) cos (x)

Vereinfache

sin^{4} (x) cos (x) - sin^{6} (x) cos (x) : sin^{4} (x) cos^{3} (x)

= sin^{4} (x) cos^{3} (x)

\frac{d}{d x} (e^{x} - cos (x))

d er i v a t i v e y = (2 x + 1) (x + 5)^{3}

n = 0 \sum \infty (- 1)^{n} (2^{n})

d er i v a t i v e y = 30 e^{- 0.0000323 (1600)}

\frac{\partial}{\partial x} (tan (\frac{y}{x}))