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

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

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Identify function components: Identify the function and its components. We have y = 2^(-x^2), which is an exponential function with a negative quadratic exponent.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 2^u and the inner function is u = -x^2.Differentiate outer function: Differentiate the outer function with respect to u. The derivative of 2^u with respect to u is (2^u * ln(2)), where ln(2) is the natural logarithm of 2.Differentiate inner function: Differentiate the inner function with respect to x. The derivative of -x^2 with respect to x is -2x.Apply chain rule with derivatives: Apply the chain rule using the derivatives from steps 3 and 4. y' = d/dx[2^(-x^2)] = (2^(-x^2) * ln(2)) * (-2x)Simplify derivative expression: Simplify the expression for the derivative. y' = -2x * 2^(-x^2) * ln(2) This is the derivative of the function y with respect to x.

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

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