derivative of (x+6^7(x+3)^5)

Lösung

\frac{d}{d x} ((x + 6)^{7} (x + 3)^{5})

7 (x + 6)^{6} (x + 3)^{5} + 5 (x + 3)^{4} (x + 6)^{7}

Schritte zur Lösung

\frac{d}{d x} ((x + 6)^{7} (x + 3)^{5})

Wende die Produktregel an:

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

f = (x + 6)^{7}, g = (x + 3)^{5}

= \frac{d}{d x} ((x + 6)^{7}) (x + 3)^{5} + \frac{d}{d x} ((x + 3)^{5}) (x + 6)^{7}

\frac{d}{d x} ((x + 6)^{7}) = 7 (x + 6)^{6}

\frac{d}{d x} ((x + 3)^{5}) = 5 (x + 3)^{4}

= 7 (x + 6)^{6} (x + 3)^{5} + 5 (x + 3)^{4} (x + 6)^{7}

y^{^{'}} = \frac{( x - 3 )}{( y - 4 )}

\int x^{2} - x - 2 d x

\frac{d}{d x} (\frac{3 x + 1}{5 x ^{2} + 1})

d er i v a t i v e f (x) = \frac{sin ( x )}{x ^{3}}

x y^{^{'}} + y = 6 x^{2}, y (1) = 2