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Answer :
Final answer:
The value of y' (3) is approximately 16.778.
Explanation:
To find the derivative of the function y = 3x² + 2/x, we need to apply the power rule and the quotient rule.
First, let's find the derivative of the term 3x². Using the power rule, the derivative of 3x² is 2*3x^(2-1) = 6x.
Next, let's find the derivative of the term 2/x. Using the quotient rule, the derivative of 2/x is (2*(-1))/x^2 = -2/x^2.
Now, we can combine the derivatives of both terms to find the derivative of the entire function. The derivative of y = 3x² + 2/x is dy/dx = 6x - 2/x^2.
To evaluate the derivative at x = 3, we substitute x = 3 into the derivative expression. dy/dx = 6(3) - 2/(3^2) = 18 - 2/9 = 16.778.
Learn more about differentiation here:
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