Find the derivative of the following function. y=7^(6x^(6)-5x^(5)) Answer: y^(')=

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Find the derivative of the following function.  y=7^(6x^(6)-5x^(5)) Answer:  y^(')=

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Identify function components: Identify the function and its components. The function is y = 7^(6x^6 - 5x^5), which is an exponential function with a base of 7 and an exponent of 6x^6 - 5x^5.Use chain rule for differentiation: Recognize that to differentiate y = 7^(6x^6 - 5x^5), we need to use the chain rule for exponential functions. The chain rule states that the derivative of a^u, where a is a constant and u is a function of x, is a^u * ln(a) * u'.Differentiate exponent function: Differentiate the exponent function u(x) = 6x^6 - 5x^5. To find u'(x), we apply the power rule to each term. u'(x) = d/dx(6x^6) - d/dx(5x^5) u'(x) = 36x^5 - 25x^4Apply chain rule to find derivative: Apply the chain rule to find the derivative of y. Using the chain rule, we get y' = 7^(6x^6 - 5x^5) * ln(7) * (36x^5 - 25x^4).Simplify derivative expression: Simplify the expression for the derivative. y' = (7^(6x^6 - 5x^5)) * ln(7) * (36x^5 - 25x^4) This is the final form of the derivative.

Find the derivative of the following function. $\newline$ $y=7^{6 x^{6}-5 x^{5}}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function. $\newline$ $y=7^{6 x^{6}-5 x^{5}}$ $\newline$ Answer: $y^{\prime}=$