derivative of (x^2-4^5(3x+5)^4)

Lösung

\frac{d}{d x} ((x^{2} - 4)^{5} (3 x + 5)^{4})

10 x (x^{2} - 4)^{4} (3 x + 5)^{4} + 12 (3 x + 5)^{3} (x^{2} - 4)^{5}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 4)^{5} (3 x + 5)^{4})

Wende die Produktregel an:

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

f = (x^{2} - 4)^{5}, g = (3 x + 5)^{4}

= \frac{d}{d x} ((x^{2} - 4)^{5}) (3 x + 5)^{4} + \frac{d}{d x} ((3 x + 5)^{4}) (x^{2} - 4)^{5}

\frac{d}{d x} ((x^{2} - 4)^{5}) = 10 x (x^{2} - 4)^{4}

\frac{d}{d x} ((3 x + 5)^{4}) = 12 (3 x + 5)^{3}

= 10 x (x^{2} - 4)^{4} (3 x + 5)^{4} + 12 (3 x + 5)^{3} (x^{2} - 4)^{5}

\int \frac{5 x - 3}{( x + 1 ) ( x - 3 )} d x

(y^{2} - 2 x y + 6 x) d x - (x^{2} - 2 x y + 2) d y = 0

\int_{1}^{e^{2}} \frac{ln ^{2} ( x ^{2} )}{x} d x

\int e^{9 x} cos (4 x) d x

\int \frac{1}{csc ( 2 x )} csc (2 x) cot (2 x) d x