derivative of (-x^2-3^2sqrt(x^2+1))

Lösung

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

\frac{5 x ^{5} + 22 x ^{3} + 21 x}{x ^{2} + 1}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (- x^{2} - 3)^{2}, g = x^{2} + 1

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

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

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

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

Vereinfache

(- 4 x (- x^{2} - 3)) x^{2} + 1 + \frac{x}{x ^{2} + 1} (- x^{2} - 3)^{2} : \frac{5 x ^{5} + 22 x ^{3} + 21 x}{x ^{2} + 1}

= \frac{5 x ^{5} + 22 x ^{3} + 21 x}{x ^{2} + 1}

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

\frac{d}{d x} (tan (11 x))

\int \frac{1}{∣ x ∣ x ^{2} - 1} d x

\int \frac{x}{x ^{2} + 1} - \frac{3}{3 x + 1} d x

f (y) = 3 y^{2}