derivative of 400(15-x^2(3x-2))

Lösung

\frac{d}{d x} (400 (15 - x^{2}) (3 x - 2))

400 (- 9 x^{2} + 4 x + 45)

Schritte zur Lösung

\frac{d}{d x} (400 (15 - x^{2}) (3 x - 2))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 400 \frac{d}{d x} ((15 - x^{2}) (3 x - 2))

Wende die Produktregel an:

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

f = 15 - x^{2}, g = 3 x - 2

= 400 (\frac{d}{d x} (15 - x^{2}) (3 x - 2) + \frac{d}{d x} (3 x - 2) (15 - x^{2}))

\frac{d}{d x} (15 - x^{2}) = - 2 x

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

= 400 ((- 2 x) (3 x - 2) + 3 (15 - x^{2}))

Vereinfache

400 ((- 2 x) (3 x - 2) + 3 (15 - x^{2})) : 400 (- 9 x^{2} + 4 x + 45)

= 400 (- 9 x^{2} + 4 x + 45)

\int cos (b x) d x

\frac{d}{d x} (\frac{x ^{2}}{arccos ( x ^{2} )})

\int \frac{x ^{2}}{( 25 - x ^{2} ) ^{\frac{3}{2}}} d x

l a pl a ce t r an s f or m 2 t + 1

5 y^{^{''}} - 6 y^{^{'}} + 3 y = 2 - 3 x^{2}