derivative of e^{3x}-1-3x

Lösung

\frac{d}{d x} (e^{3 x} - 1 - 3 x)

3 e^{3 x} - 3

Schritte zur Lösung

\frac{d}{d x} (e^{3 x} - 1 - 3 x)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{3 x}) - \frac{d}{d x} (1) - \frac{d}{d x} (3 x)

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

\frac{d}{d x} (1) = 0

\frac{d}{d x} (3 x) = 3

= e^{3 x} \cdot 3 - 0 - 3

Vereinfache

= 3 e^{3 x} - 3

d er i v a t i v e f (x) = \frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 )}

t an g e n t f (x) = 2 3 x, at x = 64

\frac{d}{d x} (x^{5} - 20 x^{3} + 64 x)

\frac{d}{d x} (\frac{10 x ^{3}}{x ^{2} - 1})

\int \frac{( x ^{2} - 16 )}{x} d x