derivative y=x(1+x^2)^{10}

Lösung

ableitung von

y = x (1 + x^{2})^{10}

(1 + x^{2})^{10} + 20 x^{2} (1 + x^{2})^{9}

Schritte zur Lösung

\frac{d}{d x} (x (1 + x^{2})^{10})

Wende die Produktregel an:

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

f = x, g = (1 + x^{2})^{10}

= \frac{d x}{d x} (1 + x^{2})^{10} + \frac{d}{d x} ((1 + x^{2})^{10}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((1 + x^{2})^{10}) = 20 x (1 + x^{2})^{9}

= 1 \cdot (1 + x^{2})^{10} + 20 x (1 + x^{2})^{9} x

Vereinfache

1 \cdot (1 + x^{2})^{10} + 20 x (1 + x^{2})^{9} x : (1 + x^{2})^{10} + 20 x^{2} (1 + x^{2})^{9}

= (1 + x^{2})^{10} + 20 x^{2} (1 + x^{2})^{9}

x \to 0 - lim (\frac{x}{x})

\int (3 y - 4 y^{3})^{3} d y

t an g e n t y = ln (\frac{x}{2}), at x = 4

\int \frac{t ^{2}}{t + 1} d t

\frac{d}{d x} (l x)