Find the derivative of the following function. y=3^(-5x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=3^(-5x^(2)) Answer:  y^(')=

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Identify Functions: We are given the function y=3^(-5x^(2)). To find the derivative, we will use the chain rule, which 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.Derivative of Outer Function: First, let's identify the outer function and the inner function. The outer function is f(u) = 3^u, and the inner function is u(x) = -5x^2. We will need to take the derivative of both of these functions.Derivative of Inner Function: The derivative of the outer function f(u) = 3^u with respect to u is f'(u) = 3^u * ln(3), using the fact that the derivative of a^x with respect to x is a^x * ln(a).Apply Chain Rule: The derivative of the inner function u(x) = -5x^2 with respect to x is u'(x) = d/dx(-5x^2) = -10x.Substitute Derivatives: Now we apply the chain rule. The derivative of y with respect to x is y' = f'(u) * u'(x). Substituting the derivatives we found, we get y' = (3^(-5x^2) * ln(3)) * (-10x).Simplify Final Derivative: Simplify the expression to get the final derivative. y' = -10x * ln(3) * 3^(-5x^2).

Find the derivative of the following function. $\newline$ $y=3^{-5 x^{2}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=3−5x2 y=3^{-5 x^{2}} y=3−5x2\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=3^{-5 x^{2}}$ $\newline$ Answer: $y^{\prime}=$