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Beliebt Rechnen >

derivative y=(5x+1)^3(x-4)

Lösung

ableitung von

y = (5 x + 1)^{3} (x - 4)

Lösung

15 (5 x + 1)^{2} (x - 4) + (5 x + 1)^{3}

Schritte zur Lösung

\frac{d}{d x} ((5 x + 1)^{3} (x - 4))

Wende die Produktregel an:

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

f = (5 x + 1)^{3}, g = x - 4

= \frac{d}{d x} ((5 x + 1)^{3}) (x - 4) + \frac{d}{d x} (x - 4) (5 x + 1)^{3}

\frac{d}{d x} ((5 x + 1)^{3}) = 15 (5 x + 1)^{2}

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

= 15 (5 x + 1)^{2} (x - 4) + 1 \cdot (5 x + 1)^{3}

Vereinfache

= 15 (5 x + 1)^{2} (x - 4) + (5 x + 1)^{3}

Graph

Beliebte Beispiele

integral of x/((x^2-4))

\int \frac{x}{( x ^{2} - 4 )} d x

derivative sin(8x)

d er i v a t i v e sin (8 x)

integral from 0 to 5 of 1/(x^{13/14)}

\int_{0}^{5} \frac{1}{x ^{\frac{13}{14}}} d x

y^{''}+2y^'-2y=0

y^{^{''}} + 2 y^{^{'}} - 2 y = 0

derivative of ln(xsqrt(x^2-3))

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