derivative of x^7e^{4x}

Lösung

\frac{d}{d x} (x^{7} e^{4 x})

7 x^{6} e^{4 x} + e^{4 x} \cdot 4 x^{7}

Schritte zur Lösung

\frac{d}{d x} (x^{7} e^{4 x})

Wende die Produktregel an:

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

f = x^{7}, g = e^{4 x}

= \frac{d}{d x} (x^{7}) e^{4 x} + \frac{d}{d x} (e^{4 x}) x^{7}

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

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= 7 x^{6} e^{4 x} + e^{4 x} \cdot 4 x^{7}

\int x^{5} sin (x^{6}) d x

\frac{d}{d x} \frac{3}{( ( 56 ) ( 2 x - 1 ) ^{7} )} - \frac{1}{( ( 24 ) ( 2 x - 1 ) ^{6} )} - \frac{1}{( ( 40 ( 2 x - 1 ) ^{5} ) )}

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

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

d er i v a t i v e f (t) = 9 t sin (π t)