Home » Blog » Find a formula for the derivative of a given function

Find a formula for the derivative of a given function

by RoRi

Find a formula for the derivative of the function

    \[ f(x) = \frac{2 - \sin x}{2 - \cos x}. \]

Using the quotient rule for derivatives,

    \begin{align*} f'(x) &= \frac{(- \cos x)(2 - \cos x)- (2 - \sin x)(\sin x)}{(2- \cos x)^2} \\[8pt] &= \frac{-2 \cos x + \cos^2 x - 2 \sin x + \sin^2 x}{(2- \cos x)^2} \\[8pt] &= \frac{1 - 2(\sin x + \cos x)}{(2- \cos x)^2} \end{align*}

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):