derivative [x+(x+sin^2(x))^5]^3

Lösung

ableitung von

[x + (x + sin^{2} (x))^{5}]^{3}

3 (x + (x + sin^{2} (x))^{5})^{2} (1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x)))

Schritte zur Lösung

\frac{d}{d x} ((x + (x + sin^{2} (x))^{5})^{3})

Wende die Kettenregel an:

3 (x + (x + sin^{2} (x))^{5})^{2} \frac{d}{d x} (x + (x + sin^{2} (x))^{5})

= 3 (x + (x + sin^{2} (x))^{5})^{2} \frac{d}{d x} (x + (x + sin^{2} (x))^{5})

\frac{d}{d x} (x + (x + sin^{2} (x))^{5}) = 1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x))

= 3 (x + (x + sin^{2} (x))^{5})^{2} (1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x)))

\int \frac{tan ( x )}{cos ^{2} ( x )} d x

x \to \frac{π}{2} lim (7 sin (x))

\int y + 1 d y

\int_{- 5}^{0} 4 + 25 - x^{2} d x

x y^{^{'}} + y + 8 = 0