derivative y=(x/(3.3)+(3.3)/x)(x^2+1)

Lösung

ableitung von

y = (\frac{x}{3.3} + \frac{3.3}{x}) (x^{2} + 1)

0.90909 \dots x^{2} - \frac{3.3}{x ^{2}} + 3.60303 \dots

Schritte zur Lösung

\frac{d}{d x} ((\frac{x}{3.3} + \frac{3.3}{x}) (x^{2} + 1))

Vereinfache

(\frac{x}{3.3} + \frac{3.3}{x}) (x^{2} + 1) : (0.30303 \dots x + \frac{3.3}{x}) (x^{2} + 1)

= \frac{d}{d x} ((0.30303 \dots x + \frac{3.3}{x}) (x^{2} + 1))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 0.30303 \dots x + \frac{3.3}{x}, g = x^{2} + 1

= \frac{d}{d x} (0.30303 \dots x + \frac{3.3}{x}) (x^{2} + 1) + \frac{d}{d x} (x^{2} + 1) (0.30303 \dots x + \frac{3.3}{x})

\frac{d}{d x} (0.30303 \dots x + \frac{3.3}{x}) = 0.30303 \dots - \frac{3.3}{x ^{2}}

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

= (0.30303 \dots - \frac{3.3}{x ^{2}}) (x^{2} + 1) + 2 x (0.30303 \dots x + \frac{3.3}{x})

Vereinfache

(0.30303 \dots - \frac{3.3}{x ^{2}}) (x^{2} + 1) + 2 x (0.30303 \dots x + \frac{3.3}{x}) : 0.90909 \dots x^{2} - \frac{3.3}{x ^{2}} + 3.60303 \dots

= 0.90909 \dots x^{2} - \frac{3.3}{x ^{2}} + 3.60303 \dots

x \to + 2 lim (2 + 3)

\int (1 + 20 w) w d w

\int \frac{x ^{2}}{( 16 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (e^{3 x} \cdot 3)

\int cos (6 y) - cos (- 6 y) d y