Find the second derivative of the function y = (2x3+4) / (5x-6)2 using the quotient rule twice.

May 23, 2026Mathematics

ScanSolve AI Answer

May 23, 2026

Answer

2x^3+4 $and$ v = (5x-6)^2$.

To find the second derivative $\frac{d^2y}{dx^2}$ of the function $y = \frac{2x^3+4}{(5x-6)^2}$ , we will use the quotient rule twice. The quotient rule states that if $y = \frac{u}{v}$ , then $\frac{dy}{dx} = \frac{u'v - uv'}{v^2}$ .

Step 1: Find the first derivative, $\frac{dy}{dx}$ . Let $u = 2x^3+4$ and $v = (5x-6)^2$ . First, find the derivatives of $u$ and $v$ : $u' = \frac{d}{dx}(2x^3+4) =

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To find the second derivative (d^2y)/(dx^2) of the function y = (2x^3+4)/((5x-6)^2), we will use the quotient rule twice.

Asked on May 23, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 23, 2026

To find the second derivative (d^2y)/(dx^2) of the function y = (2x^3+4)/((5x-6)^2), we will use the quotient rule twice. The quotient rule states that if y = (u)/(v), then (dy)/(dx) = (u'v - uv')/(v^2). Step 1: Find the first derivative, (dy)/(dx). Let u = 2x^3+4 and v = (5x-6)^2. First, find the derivatives of u and v: $u' = (d)/(dx)(2x^3+4) =