Find the derivative of the following function. y=e^(x^(5)-6x^(4)) Answer: y^(')=

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Find the derivative of the following function.  y=e^(x^(5)-6x^(4)) Answer:  y^(')=

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Identify Function Components: Identify the function and its components for differentiation. The function is y = e^(x^(5) - 6x^(4)). This is an exponential function with a composite exponent.Apply Chain Rule: Apply the chain rule for differentiation, 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. The outer function is e^u, where u = x^(5) - 6x^(4), and the inner function is u(x) = x^(5) - 6x^(4).Derivative of Outer Function: Find the derivative of the outer function with respect to u, which is e^u. The derivative of e^u with respect to u is e^u.Derivative of Inner Function: Find the derivative of the inner function u(x) = x^(5) - 6x^(4) with respect to x. We will use the power rule, which states that the derivative of x^n with respect to x is n*x^(n-1).Differentiate x^5: Differentiate the first term of the inner function, x^(5). Using the power rule, the derivative of x^(5) is 5*x^(4).Differentiate -6x^4: Differentiate the second term of the inner function, -6x^(4). Using the power rule, the derivative of -6x^(4) is -24*x^(3).Combine Inner Function Derivatives: Combine the derivatives of the terms of the inner function to find the derivative of u(x). u'(x) = 5*x^(4) - 24*x^(3).Apply Chain Rule for y': Apply the chain rule to find the derivative of y with respect to x. y' = (derivative of outer function evaluated at inner function) * (derivative of inner function). y' = e^(x^(5) - 6x^(4)) * (5*x^(4) - 24*x^(3)).

Find the derivative of the following function. $\newline$ $y=e^{x^{5}-6 x^{4}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=ex5−6x4 y=e^{x^{5}-6 x^{4}} y=ex5−6x4\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=e^{x^{5}-6 x^{4}}$ $\newline$ Answer: $y^{\prime}=$