Given the function y=(-1+2x)(-7x^(-3)-3+3x), find (dy)/(dx) in any form. Answer: (dy)/(dx)=

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Given the function  y=(-1+2x)(-7x^(-3)-3+3x), find  (dy)/(dx) in any form. Answer:  (dy)/(dx)=

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Apply Product Rule: First, we need to apply the product rule for differentiation, 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. Let's denote the first function as u(x) = -1 + 2x and the second function as v(x) = -7x^(-3) - 3 + 3x.Find Derivative of u(x): Now, we find the derivative of u(x) with respect to x. The derivative of a constant is 0, and the derivative of 2x with respect to x is 2. So, the derivative of u(x) is u'(x) = 0 + 2 = 2.Find Derivative of v(x): Next, we find the derivative of v(x) with respect to x. The derivative of -7x^(-3) is 21x^(-4), the derivative of -3 is 0, and the derivative of 3x is 3. So, the derivative of v(x) is v'(x) = 21x^(-4) + 0 + 3.Apply Product Rule: Now we apply the product rule: (dy)/(dx) = u'(x)v(x) + u(x)v'(x). Substituting the derivatives we found, we get (dy)/(dx) = 2(-7x^(-3) - 3 + 3x) + (-1 + 2x)(21x^(-4) + 3).Simplify Expression: We simplify the expression by distributing the derivatives within the parentheses: (dy)/(dx) = -14x^(-3) - 6 + 6x + (-21x^(-4) + 42x^(-3) + 3 - 6x).Combine Like Terms: Combine like terms to simplify the expression further: (dy)/(dx) = -14x^(-3) + 42x^(-3) - 21x^(-4) - 6x - 6 + 3.Final Result: After combining like terms, we get (dy)/(dx) = 28x^(-3) - 21x^(-4) - 6x - 3.

Given the function $y=(-1+2 x)\left(-7 x^{-3}-3+3 x\right)$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$

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Given the function y=(−1+2x)(−7x−3−3+3x) y=(-1+2 x)\left(-7 x^{-3}-3+3 x\right) y=(−1+2x)(−7x−3−3+3x), find dydx \frac{d y}{d x} dxdy​ in any form.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

Given the function $y=(-1+2 x)\left(-7 x^{-3}-3+3 x\right)$ , find $\frac{d y}{d x}$ in any form. $\newline$ Answer: $\frac{d y}{d x}=$