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Beliebt Rechnen >

derivative of ln(3x-e^{-2x})

Lösung

\frac{d}{d x} (ln (3 x) - e^{- 2 x})

Lösung

\frac{1}{x} + 2 e^{- 2 x}

Schritte zur Lösung

\frac{d}{d x} (ln (3 x) - e^{- 2 x})

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

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

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

Vereinfache

= \frac{1}{x} + 2 e^{- 2 x}

Graph

Beliebte Beispiele

integral of (cot(bx)+tan(bx))^2

\int (cot (b x) + tan (b x))^{2} d x

tangent f(x)=x^2,\at x=2x-1

t an g e n t f (x) = x^{2}, at x = 2 x - 1

d/(dy)(sqrt(1-y^2))

\frac{d}{d y} (1 - y^{2})

fläche y=x^{1/2},x=0,x=1

a re a y = x^{\frac{1}{2}}, x = 0, x = 1

sum from n=1 to infinity of 5/(e^{2n)}

n = 1 \sum \infty \frac{5}{e ^{2 n}}