Find the derivative of the following function. y=7^(9x^(4)+4x^(3)) Answer: y^(')=

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Find the derivative of the following function.  y=7^(9x^(4)+4x^(3)) Answer:  y^(')=

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Find Derivative Function: We need to find the derivative of the function y=7^(9x^(4)+4x^(3)). To do this, 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.Define Inner Function: Let's denote the inner function as u=9x^(4)+4x^(3). The function y can then be written as y=7^u.Derivative with Respect to Inner Function: The derivative of y with respect to u, using the exponential rule, is dy/du = 7^u * ln(7).Find Derivative of Inner Function: Now we need to find the derivative of u with respect to x, which is du/dx = 36x^(3) + 12x^(2).Apply Chain Rule: Using the chain rule, the derivative of y with respect to x is dy/dx = dy/du * du/dx.Substitute Expressions: Substitute the expressions for dy/du and du/dx into the chain rule formula to get dy/dx = (7^u * ln(7)) * (36x^(3) + 12x^(2)).Substitute Back Expression: Now we need to substitute back the expression for u into the derivative to get dy/dx in terms of x. So, dy/dx = (7^(9x^(4)+4x^(3)) * ln(7)) * (36x^(3) + 12x^(2)).Simplify Final Derivative: Simplify the expression to get the final derivative: y^(') = (7^(9x^(4)+4x^(3)) * ln(7)) * (36x^(3) + 12x^(2)).

Find the derivative of the following function. $\newline$ $y=7^{9 x^{4}+4 x^{3}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function. $\newline$ $y=7^{9 x^{4}+4 x^{3}}$ $\newline$ Answer: $y^{\prime}=$