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Beliebt Rechnen >

derivative of x^3(4-x)

Lösung

\frac{d}{d x} (x^{3} (4 - x))

Lösung

12 x^{2} - 4 x^{3}

Schritte zur Lösung

\frac{d}{d x} (x^{3} (4 - x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = 4 - x

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

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

\frac{d}{d x} (4 - x) = - 1

= 3 x^{2} (4 - x) + (- 1) x^{3}

Vereinfache

3 x^{2} (4 - x) + (- 1) x^{3} : 12 x^{2} - 4 x^{3}

= 12 x^{2} - 4 x^{3}

Graph

Beliebte Beispiele

sum from n=0 to infinity of 4/(n(n+2))

n = 0 \sum \infty \frac{4}{n ( n + 2 )}

sum from n=0 to infinity of ((5^n))/(n!)

n = 0 \sum \infty \frac{( 5 ^{n} )}{n !}

derivative tan^2(θ)

d er i v a t i v e tan^{2} (θ)

integral of (w^2)/((w^2+7)^2)

\int \frac{w ^{2}}{( w ^{2} + 7 ) ^{2}} d w

y^'=-(2x)/y ,y(1)=10

y^{^{'}} = - \frac{2 x}{y}, y (1) = 10