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In Exercises 3–24, use the rules of differentiation to find the derivative of the function. y=x212cosx

Short Answer

Expert verified
The derivative of the function y=x212cosx is y=2x+12sinx.

Step by step solution

01

Differentiate the power function

The function y involves a term x2, which is a power function. The rule for the derivative of a power function xn is nxn1. Here, n is 2. Therefore, applying the rule to x2, we get the derivative as 2x21 or 2x.
02

Differentiate the cosine function

The function y also has a term 12cosx, which includes a cosine function. The derivative of cosx is sinx. However, since it is multiplied by 12, the derivative becomes (12sinx), which simplifies to 12sinx.
03

Combine the derivatives

Now that both parts of the function have been differentiated, they need to be combined to get the derivative of the overall function. Combining the derivatives from Steps 1 and 2, we get the derivative of y as 2x+12sinx.

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