derivative of (9x^2-15xe^x)

Lösung

\frac{d}{d x} ((9 x^{2} - 15 x) e^{x})

9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((9 x^{2} - 15 x) e^{x})

Wende die Produktregel an:

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

f = 9 x^{2} - 15 x, g = e^{x}

= \frac{d}{d x} (9 x^{2} - 15 x) e^{x} + \frac{d}{d x} (e^{x}) (9 x^{2} - 15 x)

\frac{d}{d x} (9 x^{2} - 15 x) = 18 x - 15

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

= (18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x)

Vereinfache

(18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x) : 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

= 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

\int \frac{1}{9 sin ^{2} ( x )} d x

x \to 0 lim (\frac{tan ( 4 x )}{tan ( 9 x )})

x \to 1 lim (\frac{( x ^{7 a} - 7 a x + 7 a - 1 )}{( x - 1 ) ^{2}})

\int \frac{1}{( x + 8 ) ^{2}} d x

x \to 1 + lim (x^{(\frac{1}{1 - x})})