Let y=(3x-2)^(4). Find (d^(2)y)/(dx^(2)). (d^(2)y)/(dx^(2))=

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Let  y=(3x-2)^(4). Find  (d^(2)y)/(dx^(2)).  (d^(2)y)/(dx^(2))=

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Find First Derivative: To find the second derivative of y with respect to x, we first need to find the first derivative using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is u^4 and the inner function is u = 3x - 2.Simplify First Derivative: First, we differentiate u^4 with respect to u to get 4u^3. Then we differentiate the inner function 3x - 2 with respect to x to get 3. Applying the chain rule, we multiply these two results to get the first derivative of y with respect to x: dy/dx = 4 * (3x - 2)^3 * 3.Find Second Derivative: Now we simplify the first derivative: dy/dx = 12 * (3x - 2)^3.Apply Chain Rule Again: Next, we need to find the second derivative, which is the derivative of the first derivative. We will again use the chain rule. This time, the outer function is v^3 where v = 3x - 2, and the inner function is still 3x - 2.Substitute Back into Expression: Differentiating v^3 with respect to v gives us 3v^2. Differentiating the inner function 3x - 2 with respect to x again gives us 3. Applying the chain rule to the first derivative, we get the second derivative: d^2y/dx^2 = 3 * 3v^2 * 3.Simplify Second Derivative: Substitute v = 3x - 2 back into the expression for the second derivative: d^2y/dx^2 = 3 * 3 * (3x - 2)^2 * 3.Now we simplify the second derivative: d^2y/dx^2 = 27 * (3x - 2)^2.

Let $y=(3 x-2)^{4}$ . $\newline$ Find $\frac{d^{2} y}{d x^{2}}$ . $\newline$ $\frac{d^{2} y}{d x^{2}}=$

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Let y=(3x−2)4 y=(3 x-2)^{4} y=(3x−2)4.\newlineFind d2ydx2 \frac{d^{2} y}{d x^{2}} dx2d2y​.\newlined2ydx2= \frac{d^{2} y}{d x^{2}}= dx2d2y​=

Let $y=(3 x-2)^{4}$ . $\newline$ Find $\frac{d^{2} y}{d x^{2}}$ . $\newline$ $\frac{d^{2} y}{d x^{2}}=$