Find the derivative of the following function. y=e^(7x^(3)) Answer: y^(')=

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Find the derivative of the following function.  y=e^(7x^(3)) Answer:  y^(')=

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Identify Functions: We are given the function y=e^(7x^(3)). 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.Differentiate Outer Function: First, let's identify the outer function and the inner function. The outer function is e^u, where u is the inner function. The inner function is 7x^(3).Differentiate Inner Function: Now, we differentiate the outer function with respect to the inner function u. The derivative of e^u with respect to u is e^u.Apply Chain Rule: Next, we differentiate the inner function 7x^(3) with respect to x. Using the power rule, the derivative of x^(n) with respect to x is n*x^(n-1), so the derivative of 7x^(3) is 3*7*x^(3-1) which simplifies to 21x^(2).Final Derivative: Now we apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. This gives us the derivative of y with respect to x as e^(7x^(3)) * 21x^(2).Therefore, the derivative of the function y=e^(7x^(3)) is y' = 21x^(2)e^(7x^(3)).

Find the derivative of the following function. $\newline$ $y=e^{7 x^{3}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=e7x3 y=e^{7 x^{3}} y=e7x3\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=e^{7 x^{3}}$ $\newline$ Answer: $y^{\prime}=$