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Beliebt Rechnen >

derivative of (x-4ax^2+ln(x/4)bx^4)

Lösung

\frac{d}{d x} ((x - 4) \cdot a x^{2} + ln (\frac{x}{4}) \cdot b x^{4})

Lösung

a (3 x^{2} - 8 x) + b (x^{3} + 4 x^{3} ln (\frac{x}{4}))

Schritte zur Lösung

\frac{d}{d x} ((x - 4) a x^{2} + ln (\frac{x}{4}) b x^{4})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} ((x - 4) a x^{2}) + \frac{d}{d x} (ln (\frac{x}{4}) b x^{4})

\frac{d}{d x} ((x - 4) a x^{2}) = a (3 x^{2} - 8 x)

\frac{d}{d x} (ln (\frac{x}{4}) b x^{4}) = b (x^{3} + 4 x^{3} ln (\frac{x}{4}))

= a (3 x^{2} - 8 x) + b (x^{3} + 4 x^{3} ln (\frac{x}{4}))

Graph

Beliebte Beispiele

integral of cos(8t)

\int cos (8 t) d t

integral of (x^2+2x-1)/(x(x+1)(x-1))

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

y^'=3x+y,y(0)=7

y^{^{'}} = 3 x + y, y (0) = 7

limit as x approaches 0+of x^2csc^2(x)

x \to 0 + lim (x^{2} csc^{2} (x))

x(dy)/(dx)=y-1/y

x \frac{d y}{d x} = y - \frac{1}{y}