Consider . (i) Differentiate with respect to . (ii) Show that . (iii) Find all values…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider h(x)=4cot⁡x−2ln⁡x+6cos⁡xh(x)=4\cot x-2\ln x+6\cos x. (i) Differentiate h(x)h(x) with respect to xx. (ii) Show that h′(x)=−4csc⁡2x−2x−6sin⁡xh'(x)=-4\csc^{2}x-\dfrac{2}{x}-6\sin x. (iii) Find all values of xx in (0,π)(0,\pi) for which h′(x)=0h'(x)=0.

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