What is (d^2)/(dx^2)((y)(3x-1)^3) ?

The answer to (d^2)/(dx^2)((y)(3x-1)^3) is (d^2y)/(dx^2)(3x-1)^3+18(dy)/(dx)(3x-1)^2+162xy-54y

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(d^2)/(dx^2)((y)(3x-1)^3)

\frac{d ^{2}}{d x ^{2}} ((y) (3 x - 1)^{3})

\frac{d ^{2} y}{d x ^{2}} (3 x - 1)^{3} + 18 \frac{d y}{d x} (3 x - 1)^{2} + 162 x y - 54 y

Solution steps

\frac{d ^{2}}{d x ^{2}} ((y) (3 x - 1)^{3})

\frac{d}{d x} (y (3 x - 1)^{3}) = \frac{d y}{d x} (3 x - 1)^{3} + 9 (3 x - 1)^{2} y

= \frac{d}{d x} (\frac{d y}{d x} (3 x - 1)^{3} + 9 (3 x - 1)^{2} y)

\frac{d}{d x} (\frac{d y}{d x} (3 x - 1)^{3} + 9 (3 x - 1)^{2} y) = \frac{d ^{2} y}{d x ^{2}} (3 x - 1)^{3} + 18 \frac{d y}{d x} (3 x - 1)^{2} + 162 x y - 54 y

= \frac{d ^{2} y}{d x ^{2}} (3 x - 1)^{3} + 18 \frac{d y}{d x} (3 x - 1)^{2} + 162 x y - 54 y

\frac{( 4 + x ) ( x - 2 )}{x}

(1 - x + 2)^{2}

\frac{2 ^{i} ( 2 ^{k - i} - 1 ) ^{2}}{2 ^{k} - 1}

12 (\frac{2}{3} x + 7)

(a + b c) (a - b c)

What is (d^2)/(dx^2)((y)(3x-1)^3) ?
The answer to (d^2)/(dx^2)((y)(3x-1)^3) is (d^2y)/(dx^2)(3x-1)^3+18(dy)/(dx)(3x-1)^2+162xy-54y