Find the derivative of the following function. y=e^(9x^(3)-2x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=e^(9x^(3)-2x^(2)) Answer:  y^(')=

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Identify Function: Identify the function and its components. The function is y = e^(9x^3 - 2x^2). This is an exponential function where the exponent is a polynomial.Apply Chain Rule: Apply the chain rule for differentiation. 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 e^u and the inner function is u = 9x^3 - 2x^2.Differentiate Outer Function: Differentiate the outer function with respect to the inner function u. The derivative of e^u with respect to u is e^u. So, (d/du)(e^u) = e^u.Differentiate Inner Function: Differentiate the inner function u = 9x^3 - 2x^2 with respect to x. Using the power rule, the derivative of 9x^3 is 27x^2 and the derivative of -2x^2 is -4x. So, (d/dx)(9x^3 - 2x^2) = 27x^2 - 4x.Combine Derivatives: Combine the derivatives using the chain rule. The derivative of y with respect to x is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. So, y' = e^(9x^3 - 2x^2) * (27x^2 - 4x).

Find the derivative of the following function. $\newline$ $y=e^{9 x^{3}-2 x^{2}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function. $\newline$ $y=e^{9 x^{3}-2 x^{2}}$ $\newline$ Answer: $y^{\prime}=$