derivative of x^3ln(1+x^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

\int_{0}^{3} \frac{x - 2}{x ^{2} - 3 x - 4} d x

x y^{6} y^{^{'}} = x^{7} + y^{7}

\int_{1}^{4} \frac{5}{x ^{2} + 4 x + 4} d x

\frac{\partial}{\partial x} (4 x^{3} y^{2} + 1)

d er i v a t i v e y = \frac{( x ^{7} - 4 x ^{3} + 12 x )}{x ^{3}}