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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

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

x \to \infty lim ((\frac{13 x}{13 x + 3})^{5 x})

\int \frac{2 x - 4}{( x ^{2} - 4 x + 7 ) ^{2}} d x

l a pl a ce t r an s f or m (- 2)^{t - 1}

\int \frac{3 x ( e ^{- 2 x} - 7 x )}{5} d x