how do you do this problem: arctan(y^9)
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You're expected to know that the derivative of $\displaystyle \arctan x$ equals $\displaystyle \frac1{1+x^2}.$ By the Chain Rule, we have that the derivative of $\displaystyle \arctan y^9$ equals $\displaystyle \frac1{1+y^{18}}\cdot(y^9)'.$
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