Find k'(x). k(x)=e^(x)(-x^(3//5)

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Identify Components Requiring Product Rule: Identify the components of the function k(x) that will require the use of the product rule for differentiation. The function k(x) = e^(x)(-x^(3/5)) is a product of two functions: e^(x) and (-x^(3/5)). The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.Differentiate First Function: Differentiate the first function, which is e^(x). The derivative of e^(x) with respect to x is e^(x).Differentiate Second Function: Differentiate the second function, which is -x^(3/5). Using the power rule, the derivative of -x^(3/5) with respect to x is (3/5)(-x^(-2/5)).Apply Product Rule: Apply the product rule. Using the product rule, the derivative of k(x) is: k'(x) = e^(x) * (3/5)(-x^(-2/5)) + e^(x) * (-x^(3/5))Simplify Expression: Simplify the expression. k'(x) = (3/5)(-e^(x)x^(-2/5)) - e^(x)x^(3/5) This can be further simplified by factoring out e^(x): k'(x) = e^(x)((3/5)(-x^(-2/5)) - x^(3/5))Check for Errors: Check for any mathematical errors in the differentiation process. Reviewing the steps, the differentiation was done correctly using the product rule and the power rule. There are no mathematical errors.

Find $k'(x)$ . $\newline$ $k(x)=e^{x}(-x^{\frac{3}{5}})$

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Find $k'(x)$ . $\newline$ $k(x)=e^{x}(-x^{\frac{3}{5}})$