derivative of (3x^2-6x+10(x^3))

Lösung

\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

15 x^{4} - 24 x^{3} + 30 x^{2}

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} - 6 x + 10) (x^{3}))

Wende die Produktregel an:

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

f = 3 x^{2} - 6 x + 10, g = x^{3}

= \frac{d}{d x} (3 x^{2} - 6 x + 10) x^{3} + \frac{d}{d x} (x^{3}) (3 x^{2} - 6 x + 10)

\frac{d}{d x} (3 x^{2} - 6 x + 10) = 6 x - 6

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

= (6 x - 6) x^{3} + 3 x^{2} (3 x^{2} - 6 x + 10)

Vereinfache

(6 x - 6) x^{3} + 3 x^{2} (3 x^{2} - 6 x + 10) : 15 x^{4} - 24 x^{3} + 30 x^{2}

= 15 x^{4} - 24 x^{3} + 30 x^{2}

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{(- x)} sec (2 x)

\frac{d}{d x} (\frac{12}{x ^{5}} - \frac{7}{5 x})

\frac{d}{d x} (e^{\frac{x}{y}} ln (\frac{x ^{2}}{y}))

(x y - x) d x + (x y + y) d y = 0

\frac{d y}{d x} = e^{2 x - 3 y}