(d^2)/(dx^2)(({f}(x))(4x^3-6x^2+3))

解

\frac{d ^{2}}{d x ^{2}} ((f (x)) (4 x^{3} - 6 x^{2} + 3))

\frac{d ^{2}}{d x ^{2}} (f (x)) (4 x^{3} - 6 x^{2} + 3) + 2 \frac{d}{d x} (f (x)) (12 x^{2} - 12 x) + (24 x - 12) f (x)

解答ステップ

\frac{d ^{2}}{d x ^{2}} ((f (x)) (4 x^{3} - 6 x^{2} + 3))

\frac{d}{d x} (f (x) (4 x^{3} - 6 x^{2} + 3)) = \frac{d}{d x} (f (x)) (4 x^{3} - 6 x^{2} + 3) + (12 x^{2} - 12 x) f (x)

= \frac{d}{d x} (\frac{d}{d x} (f (x)) (4 x^{3} - 6 x^{2} + 3) + (12 x^{2} - 12 x) f (x))

\frac{d}{d x} (\frac{d}{d x} (f (x)) (4 x^{3} - 6 x^{2} + 3) + (12 x^{2} - 12 x) f (x)) = \frac{d ^{2}}{d x ^{2}} (f (x)) (4 x^{3} - 6 x^{2} + 3) + 2 \frac{d}{d x} (f (x)) (12 x^{2} - 12 x) + (24 x - 12) f (x)

= \frac{d ^{2}}{d x ^{2}} (f (x)) (4 x^{3} - 6 x^{2} + 3) + 2 \frac{d}{d x} (f (x)) (12 x^{2} - 12 x) + (24 x - 12) f (x)