derivative [x+(x+sin^2(x))^4]^3

Lösung

ableitung von

[x + (x + sin^{2} (x))^{4}]^{3}

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

Schritte zur Lösung

\frac{d}{d x} ((x + (x + sin^{2} (x))^{4})^{3})

Wende die Kettenregel an:

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

= 3 (x + (x + sin^{2} (x))^{4})^{2} \frac{d}{d x} (x + (x + sin^{2} (x))^{4})

\frac{d}{d x} (x + (x + sin^{2} (x))^{4}) = 1 + 4 (x + sin^{2} (x))^{3} (1 + sin (2 x))

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

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

\frac{d}{d x} (x^{4} ln (9 x))

\frac{d}{d x} (2 x^{2} - 5 x + 1)

y^{^{'}} + 3 x^{- 1} y = x^{2}

\int_{1}^{2} x^{4} ln (x) d x