Find the derivative of the following function. y=7^(-x^(4)) Answer: y^(')=

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Find the derivative of the following function.  y=7^(-x^(4)) Answer:  y^(')=

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Given Function: We are given the function y=7^(-x^(4)). To find the derivative, we will use the chain rule and the exponential rule for derivatives.Rewriting with Natural Log: Let's rewrite the function using the natural logarithm to make the differentiation easier. We can express 7 as e^(ln(7)), so the function becomes y = (e^(ln(7)))^(-x^(4)).Apply Chain Rule: Now, apply the chain rule. The outer function is e^(u) where u = ln(7)*(-x^(4)), and the inner function is u = ln(7)*(-x^(4)). We need to find the derivative of the outer function with respect to u, and then multiply it by the derivative of u with respect to x.Derivative of Outer Function: The derivative of e^(u) with respect to u is e^(u). So the derivative of the outer function with respect to u is e^(ln(7)*(-x^(4))).Derivative of Inner Function: Now, we differentiate the inner function u = ln(7)*(-x^(4)) with respect to x. The constant ln(7) remains as it is, and the derivative of -x^(4) with respect to x is -4x^(4-1) or -4x^3.Multiply Derivatives: Multiplying the derivative of the outer function by the derivative of the inner function, we get the derivative of y with respect to x: dy/dx = e^(ln(7)*(-x^(4))) * ln(7) * (-4x^3).Simplify Expression: We can simplify the expression by remembering that e^(ln(7)) is just 7. So the derivative of y with respect to x is dy/dx = 7^(-x^(4)) * ln(7) * (-4x^3).Final Derivative: Finally, we can write the derivative in its simplest form: y' = -4 * ln(7) * x^3 * 7^(-x^(4)).

Find the derivative of the following function. $\newline$ $y=7^{-x^{4}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function. $\newline$ $y=7^{-x^{4}}$ $\newline$ Answer: $y^{\prime}=$