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Beliebt Rechnen >

derivative of e^{rx}r

Lösung

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

Lösung

e^{r x} (x \frac{d r}{d x} + r) r + \frac{d r}{d x} e^{r x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = e^{r x}, g = r

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

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

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

Beliebte Beispiele

tangent f(x)=x^2-5x+5,\at x=6

t an g e n t f (x) = x^{2} - 5 x + 5, at x = 6

taylor x^2cos(x),0.1

t a y l or x^{2} cos (x), 0.1

derivative f(x)=-25x^2+150x-182

d er i v a t i v e f (x) = - 25 x^{2} + 150 x - 182

integral of csc^3(2x)cot^3(2x)

\int csc^{3} (2 x) cot^{3} (2 x) d x

(tdy)/(dt)-3y=sqrt(t)

\frac{t d y}{d t} - 3 y = t