Find the derivative of the following function. y=6^(-4x^(2)) Answer: y^(')=

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Find the derivative of the following function.  y=6^(-4x^(2)) Answer:  y^(')=

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Rewrite function: We are given the function y=6^(-4x^(2)). To find the derivative, we will use the chain rule and the exponential rule for differentiation.Apply chain rule: First, let's rewrite the function using the natural exponential function for convenience in differentiation: y = e^(ln(6)*(-4x^2))Differentiate with ln(6): Now, let's differentiate both sides of the equation with respect to x using the chain rule: dy/dx = d/dx [e^(ln(6)*(-4x^2))]Simplify exponent differentiation: Applying the chain rule, we get: dy/dx = e^(ln(6)*(-4x^2)) * d/dx [ln(6)*(-4x^2)]Differentiate -4x^2: Since ln(6) is a constant, we can simplify the differentiation of the exponent as follows: dy/dx = e^(ln(6)*(-4x^2)) * ln(6) * d/dx [-4x^2]Substitute back derivative: Now, differentiate -4x^2 with respect to x: d/dx [-4x^2] = -4 * 2x = -8xRewrite in terms of y: Substitute the derivative of -4x^2 back into the equation: dy/dx = e^(ln(6)*(-4x^2)) * ln(6) * (-8x)Substitute original y: Finally, we can rewrite the derivative in terms of the original function y: dy/dx = y * ln(6) * (-8x)Simplify final answer: Now, we can substitute back the original expression for y to get the final derivative: dy/dx = 6^(-4x^2) * ln(6) * (-8x)Simplify the expression to get the final answer: y' = -8x * ln(6) * 6^(-4x^2)

Find the derivative of the following function. $\newline$ $y=6^{-4 x^{2}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=6−4x2 y=6^{-4 x^{2}} y=6−4x2\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=6^{-4 x^{2}}$ $\newline$ Answer: $y^{\prime}=$