derivative f(x)=e^x(x+xsqrt(x))

Lösung

ableitung von

f (x) = e^{x} (x + x x)

e^{x} (x + x^{\frac{3}{2}}) + (1 + \frac{3 x}{2}) e^{x}

Schritte zur Lösung

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

Vereinfache

e^{x} (x + x x) : e^{x} (x + x^{\frac{3}{2}})

= \frac{d}{d x} (e^{x} (x + x^{\frac{3}{2}}))

Wende die Produktregel an:

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

f = e^{x}, g = x + x^{\frac{3}{2}}

= \frac{d}{d x} (e^{x}) (x + x^{\frac{3}{2}}) + \frac{d}{d x} (x + x^{\frac{3}{2}}) e^{x}

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

\frac{d}{d x} (x + x^{\frac{3}{2}}) = 1 + \frac{3 x}{2}

= e^{x} (x + x^{\frac{3}{2}}) + (1 + \frac{3 x}{2}) e^{x}

\frac{d y}{d x} = y - y^{2}

t an g e n t f (x) = - x^{3}, (1, - 1)

d er i v a t i v e x^{2} - 5 x + 5

\int - 7 tan^{3} (x) d x

\int 2 t e^{t} d t