For the following equation, find (dy)/(dx). y=-5x^(3)+7x+6 Answer: (dy)/(dx)=

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For the following equation, find  (dy)/(dx).  y=-5x^(3)+7x+6 Answer:  (dy)/(dx)=

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Given Function: Given the function y = -5x^3 + 7x + 6, we need to find the derivative of y with respect to x, denoted as (dy)/(dx). To do this, we will use the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).Differentiate -5x^3: First, we differentiate the term -5x^3. Using the power rule, the derivative of -5x^3 with respect to x is -5 * 3x^(3-1) = -15x^2.Differentiate 7x: Next, we differentiate the term 7x. The derivative of 7x with respect to x is 7, since the power of x is 1 and 1*x^(1-1) = 1*x^0 = 1.Differentiate Constant: Finally, we differentiate the constant term 6. The derivative of a constant with respect to x is 0, because constants do not change as x changes.Combine Derivatives: Combining the derivatives of all terms, we get (dy)/(dx) = -15x^2 + 7 + 0.Simplify Final Derivative: Simplifying the expression, we see that the +0 is unnecessary and can be omitted. Therefore, the final simplified form of the derivative is (dy)/(dx) = -15x^2 + 7.

For the following equation, find $\frac{d y}{d x}$ . $\newline$ $y=-5 x^{3}+7 x+6$ $\newline$ Answer: $\frac{d y}{d x}=$

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For the following equation, find dydx \frac{d y}{d x} dxdy​.\newliney=−5x3+7x+6 y=-5 x^{3}+7 x+6 y=−5x3+7x+6\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

For the following equation, find $\frac{d y}{d x}$ . $\newline$ $y=-5 x^{3}+7 x+6$ $\newline$ Answer: $\frac{d y}{d x}=$