Given the function y=(3+4x)(6x-5-x^(3)), find (dy)/(dx) in any form. Answer: (dy)/(dx)=

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Given the function  y=(3+4x)(6x-5-x^(3)), find  (dy)/(dx) in any form. Answer:  (dy)/(dx)=

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Given Function: We are given the function y=(3+4x)(6x-5-x^(3)). To find the derivative dy/dx, we will use the product rule, which states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.Product Rule: Let's denote the first function as f(x) = 3+4x and the second function as g(x) = 6x-5-x^(3). According to the product rule, (dy)/(dx) = f'(x)g(x) + f(x)g'(x).Derivative of f(x): First, we find the derivative of f(x), which is f'(x) = d/dx(3+4x). The derivative of a constant is 0, and the derivative of 4x with respect to x is 4. Therefore, f'(x) = 0+4 = 4.Derivative of g(x): Next, we find the derivative of g(x), which is g'(x) = d/dx(6x-5-x^(3)). The derivative of 6x is 6, the derivative of -5 is 0, and the derivative of -x^(3) is -3x^(2). Therefore, g'(x) = 6-0-3x^(2) = 6-3x^(2).Apply Product Rule: Now we apply the product rule: (dy)/(dx) = f'(x)g(x) + f(x)g'(x). Substituting the derivatives we found, we get (dy)/(dx) = 4(6x-5-x^(3)) + (3+4x)(6-3x^(2)).Simplify Expression: We simplify the expression by distributing the multiplication: (dy)/(dx) = 4*6x - 4*5 - 4*x^(3) + 3*6 + 3*(-3x^(2)) + 4x*6 - 4x*3x^(2).Further Simplify: Further simplifying, we get (dy)/(dx) = 24x - 20 - 4x^(3) + 18 - 9x^(2) + 24x - 12x^(3).Combine Like Terms: Combine like terms to get the final derivative: (dy)/(dx) = (24x + 24x) - 20 + 18 - (4x^(3) + 12x^(3)) - 9x^(2).Final Derivative: After combining like terms, we have (dy)/(dx) = 48x - 2 - 16x^(3) - 9x^(2).

Given the function $y=(3+4 x)\left(6 x-5-x^{3}\right)$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$

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Given the function y=(3+4x)(6x−5−x3) y=(3+4 x)\left(6 x-5-x^{3}\right) y=(3+4x)(6x−5−x3), find dydx \frac{d y}{d x} dxdy​ in any form.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given the function $y=(3+4 x)\left(6 x-5-x^{3}\right)$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$