Find the derivative of the following function. y=7^(x^(2)-9x) Answer: y^(')=

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Find the derivative of the following function.  y=7^(x^(2)-9x) Answer:  y^(')=

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Identify Function Components: Identify the function and its components. We have y = 7^(x^2 - 9x), which is an exponential function with base 7 and an exponent that is a function of x, namely x^2 - 9x.Apply Chain Rule: Apply the chain rule for differentiation. The chain rule 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. Here, the outer function is a^u where a is a constant and u is a function of x. The derivative of a^u with respect to u is a^u * ln(a). The inner function is u(x) = x^2 - 9x. The derivative of u with respect to x is u'(x) = 2x - 9.Differentiate Outer Function: Differentiate the outer function with respect to the inner function. Let's denote the outer function as f(u) = 7^u. Then, f'(u) = 7^u * ln(7).Differentiate Inner Function: Differentiate the inner function with respect to x. We have u(x) = x^2 - 9x. The derivative u'(x) is found by differentiating each term separately: u'(x) = d/dx(x^2) - d/dx(9x) u'(x) = 2x - 9Apply Chain Rule for Derivative: Apply the chain rule to find the derivative of y with respect to x. Using the chain rule, we get: y'(x) = f'(u(x)) * u'(x) y'(x) = (7^(x^2 - 9x) * ln(7)) * (2x - 9)Simplify Derivative: Simplify the expression for the derivative. y'(x) = 7^(x^2 - 9x) * ln(7) * (2x - 9) This is the final form of the derivative.

Find the derivative of the following function. $\newline$ $y=7^{x^{2}-9 x}$ $\newline$ Answer: $y^{\prime}=$

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Find the derivative of the following function.\newliney=7x2−9x y=7^{x^{2}-9 x} y=7x2−9x\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=7^{x^{2}-9 x}$ $\newline$ Answer: $y^{\prime}=$