derivative 3x^2(x^3+1)^7

Lösung

ableitung von

3 x^{2} (x^{3} + 1)^{7}

3 (2 x (x^{3} + 1)^{7} + 21 x^{4} (x^{3} + 1)^{6})

Schritte zur Lösung

\frac{d}{d x} (3 x^{2} (x^{3} + 1)^{7})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{2} (x^{3} + 1)^{7})

Wende die Produktregel an:

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

f = x^{2}, g = (x^{3} + 1)^{7}

= 3 (\frac{d}{d x} (x^{2}) (x^{3} + 1)^{7} + \frac{d}{d x} ((x^{3} + 1)^{7}) x^{2})

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

\frac{d}{d x} ((x^{3} + 1)^{7}) = 21 x^{2} (x^{3} + 1)^{6}

= 3 (2 x (x^{3} + 1)^{7} + 21 x^{2} (x^{3} + 1)^{6} x^{2})

21 x^{2} (x^{3} + 1)^{6} x^{2} = 21 x^{4} (x^{3} + 1)^{6}

= 3 (2 x (x^{3} + 1)^{7} + 21 x^{4} (x^{3} + 1)^{6})

x \to 0 lim (\frac{sin ^{2} ( 4 x )}{x})

x \to 0 + lim (- \frac{1}{sin ( 2 x )})

l a pl a ce t r an s f or m 4 (t + 3)

\frac{d}{d x} (y x^{y - 1})

\int \frac{2 sin ( x ) cos ( x )}{1 + tan ( x )} d x