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Beliebt Rechnen >

derivative of 8xy-1/4 (x+y^4)

Lösung

\frac{d}{d x} (8 x y - \frac{1}{4} (x + y)^{4})

Lösung

8 (y + x \frac{d y}{d x}) - (1 + \frac{d y}{d x}) (x + y)^{3}

Schritte zur Lösung

\frac{d}{d x} (8 x y - \frac{1}{4} (x + y)^{4})

Vereinfache

8 x y - \frac{1}{4} (x + y)^{4} : 8 x y - \frac{( x + y ) ^{4}}{4}

= \frac{d}{d x} (8 x y - \frac{( x + y ) ^{4}}{4})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (8 x y) - \frac{d}{d x} (\frac{( x + y ) ^{4}}{4})

\frac{d}{d x} (8 x y) = 8 (y + x \frac{d y}{d x})

\frac{d}{d x} (\frac{( x + y ) ^{4}}{4}) = (1 + \frac{d y}{d x}) (x + y)^{3}

= 8 (y + x \frac{d y}{d x}) - (1 + \frac{d y}{d x}) (x + y)^{3}

Beliebte Beispiele

f(x)=x^2cos(x^2)

f (x) = x^{2} cos (x^{2})

integral of (ln(x^3))/x

\int \frac{ln ( x ^{3} )}{x} d x

limit as x approaches 2 of (2-|x|)/(2+x)

x \to 2 lim (\frac{2 - ∣ x ∣}{2 + x})

integral from-pi/3 to 0 of 3sec^3(x)

\int_{- \frac{π}{3}}^{0} 3 sec^{3} (x) d x

integral of (x+5)^2

\int (x + 5)^{2} d x