derivative of [x+(x+sin^2(x)^6]^5)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

5 (x + (x + sin^{2} (x))^{6})^{4} \frac{d}{d x} (x + (x + sin^{2} (x))^{6})

= 5 (x + (x + sin^{2} (x))^{6})^{4} \frac{d}{d x} (x + (x + sin^{2} (x))^{6})

\frac{d}{d x} (x + (x + sin^{2} (x))^{6}) = 1 + 6 (x + sin^{2} (x))^{5} (1 + sin (2 x))

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

(x^{2} - 2 y^{2}) d x + x y d y = 0

y^{^{'''}} - 6 y^{^{''}} = 3 - cos (x)

x \to 0 - lim (\frac{1}{x} - \frac{1}{e ^{x} - 1})

y^{^{'}} = 1 0^{x + y}

x \to 7 lim (2 x - 7)