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Beliebt Vorkalkül >

derivative y=3x^3+1/4 x^2

Lösung

ableitung von

y = 3 x^{3} + \frac{1}{4} x^{2}

Lösung

9 x^{2} + \frac{x}{2}

Schritte zur Lösung

\frac{d}{d x} (3 x^{3} + \frac{1}{4} x^{2})

Vereinfache

3 x^{3} + \frac{1}{4} x^{2} : 3 x^{3} + \frac{x ^{2}}{4}

= \frac{d}{d x} (3 x^{3} + \frac{x ^{2}}{4})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (\frac{x ^{2}}{4})

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

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

= 9 x^{2} + \frac{x}{2}

Graph

Beliebte Beispiele

derivative f(x)=e^x+2e^{2x}

d er i v a t i v e f (x) = e^{x} + 2 e^{2 x}

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tangent f(x)=x^2,\at x=3

t an g e n t f (x) = x^{2}, at x = 3

m = \frac{1}{2}

derivative y=x^2ln(x)

d er i v a t i v e y = x^{2} ln (x)