15. Find \( f^{\prime \prime}(x) \) if \( f(x)=\cot 5 x+x^{3} \). \[ C^{\prime}(x)=-\csc ^{2}(5 x) \cdot(5)+3 x^{2} \] 16. Let \( f(x)=(\arccos x)-3 x \). a.) Find \( f^{\prime}(x) \). b.) Find the equation of the tangent line to \( f(x) \) at the point where \( x=0 \).
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The derivative of \(\cot 5x\) is \(-\csc^2(5x) \cdot 5\) using the chain rule. The derivative of \(x^3\) is \(3x^2\). So, \( f'(x) = -5 \csc^2(5x) + 3x^2 \). Show more…
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