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

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

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Identify function: Identify the function to differentiate. We have y = 9^(-x^2). This is an exponential function with a base of 9 and an exponent of -x^2.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. Here, the outer function is 9^u and the inner function is u = -x^2.Differentiate outer function: Differentiate the outer function with respect to the inner function u. The derivative of 9^u with respect to u is 9^u * ln(9), where ln(9) is the natural logarithm of 9.Differentiate inner function: Differentiate the inner function with respect to x. The derivative of u = -x^2 with respect to x is -2x.Apply chain rule: Apply the chain rule by multiplying the derivatives from steps 3 and 4. The derivative of y with respect to x is (9^(-x^2) * ln(9)) * (-2x).Simplify expression: Simplify the expression. y' = -2x * 9^(-x^2) * ln(9).

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

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