derivative of 4^{2-2x}

Lösung

\frac{d}{d x} (4^{2 - 2 x})

- ln (2) \cdot 4^{- 2 x + 3}

Schritte zur Lösung

\frac{d}{d x} (4^{2 - 2 x})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

4^{2 - 2 x} = e^{(2 - 2 x) l n (4)}

= \frac{d}{d x} (e^{(2 - 2 x) l n (4)})

Wende die Kettenregel an:

e^{(2 - 2 x) l n (4)} \frac{d}{d x} ((2 - 2 x) ln (4))

= e^{(2 - 2 x) l n (4)} \frac{d}{d x} ((2 - 2 x) ln (4))

\frac{d}{d x} ((2 - 2 x) ln (4)) = - 4 ln (2)

= e^{(2 - 2 x) l n (4)} (- 4 ln (2))

Vereinfache

e^{(2 - 2 x) l n (4)} (- 4 ln (2)) : - ln (2) \cdot 4^{- 2 x + 3}

= - ln (2) \cdot 4^{- 2 x + 3}

\int_{0}^{1} 2 x (4 - x^{2}) d x

\frac{\partial}{\partial x} (10 x y e^{- (x^{2} + y^{2})})

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

d er i v a t i v e f (x) = tan (4 x)

l a pl a ce t r an s f or m 4