derivative [x+(x+sin^2(x))^5]^7

Lösung

ableitung von

[x + (x + sin^{2} (x))^{5}]^{7}

7 (x + (x + sin^{2} (x))^{5})^{6} (1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x)))

Schritte zur Lösung

\frac{d}{d x} ((x + (x + sin^{2} (x))^{5})^{7})

Wende die Kettenregel an:

7 (x + (x + sin^{2} (x))^{5})^{6} \frac{d}{d x} (x + (x + sin^{2} (x))^{5})

= 7 (x + (x + sin^{2} (x))^{5})^{6} \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))

= 7 (x + (x + sin^{2} (x))^{5})^{6} (1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x)))

d er i v a t i v e 6 (2 x^{3} + 3) 6 x^{2}

\int \frac{2 - 4 x ^{2}}{x - x ^{3}} d x

t an g e n t y = F - x^{2} - x, at x = - 2

d er i v a t i v e f (x) = 10 t

y^{^{'}} = x + 4 y