Find the derivative of the following function. y=3^(-8x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=3^(-8x^(2)) Answer:  y^(')=

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Identify Function Components: Identify the function and its components. We have y = 3^(-8x^(2)). This is an exponential function where the base is a constant (3) and the exponent is a function of x (-8x^(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. In this case, the outer function is f(u) = 3^u and the inner function is u(x) = -8x^(2).Differentiate Outer Function: Differentiate the outer function with respect to u. The derivative of f(u) = 3^u with respect to u is f'(u) = 3^u * ln(3), where ln(3) is the natural logarithm of 3.Differentiate Inner Function: Differentiate the inner function with respect to x. The derivative of u(x) = -8x^(2) with respect to x is u'(x) = d/dx(-8x^(2)) = -16x.Apply Chain Rule with Derivatives: Apply the chain rule using the derivatives from steps 3 and 4. y' = f'(u(x)) * u'(x) = (3^(-8x^(2)) * ln(3)) * (-16x).Simplify Derivative: Simplify the expression for the derivative. y' = -16x * 3^(-8x^(2)) * ln(3). This is the derivative of the function y with respect to x.

Find the derivative of the following function. $\newline$ $y=3^{-8 x^{2}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=3−8x2 y=3^{-8 x^{2}} y=3−8x2\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=3^{-8 x^{2}}$ $\newline$ Answer: $y^{\prime}=$