derivative (t+e^t)(3-sqrt(t))

Lösung

ableitung von

(t + e^{t}) (3 - t)

\frac{- 3 t - 2 e ^{t} t + 6 e ^{t} t - e ^{t}}{2 t} + 3

Schritte zur Lösung

\frac{d}{d t} ((t + e^{t}) (3 - t))

Wende die Produktregel an:

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

f = t + e^{t}, g = 3 - t

= \frac{d}{d t} (t + e^{t}) (3 - t) + \frac{d}{d t} (3 - t) (t + e^{t})

\frac{d}{d t} (t + e^{t}) = 1 + e^{t}

\frac{d}{d t} (3 - t) = - \frac{1}{2 t}

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

Vereinfache

(1 + e^{t}) (3 - t) + (- \frac{1}{2 t}) (t + e^{t}) : \frac{- 3 t - 2 e ^{t} t + 6 e ^{t} t - e ^{t}}{2 t} + 3

= \frac{- 3 t - 2 e ^{t} t + 6 e ^{t} t - e ^{t}}{2 t} + 3

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

\int \frac{x ^{2}}{x - 4} d x

d er i v a t i v e 5

\frac{d y}{d x} + 6 \cdot (tan (6 x)) \cdot y = 2 \cdot cos (6 x)

\int \frac{33 x ^{2}}{x ^{2} - 4} d x