3.4: Derivatives of Trigonometric Functions
- Page ID
- 143972
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Given \(y = \sin x + \cos x + 2x^3\), find \(\dfrac{dy}{dx}\).
- Given \(f(x) = 2x\sec x\), find \(\dfrac{df}{dx}\).
- Given \(g(x) = \dfrac{\tan x}{x}\), find \(\dfrac{dg}{dx}\).
- Given \(h(x) = \csc x \cot x\), find \(\dfrac{dh}{dx}\).
- Given \(y = 4\sin x - 3\sqrt{x}\), find \(y'\).
- Given \(f(x) = x\cos^2 x\), find \(f'(x)\).
- Given \(g(x) = \dfrac{\sec x}{\csc x}\), find \(g'(x)\).
- Given \(h(x) = \dfrac{(x + 1)\tan x}{1 + \cot x}\), find \(h'(x)\).
- Given \(r = \dfrac{\sec \theta}{1 + \tan \theta}\), find \(\dfrac{dr}{d\theta}\).
- Given \(x = \sin^2 t + \cos^2 t\), find \(\dfrac{dx}{dt}\).
- Given \(f(\theta) = -3(\sec^2 \theta - \tan^2 \theta)\), find \(\dfrac{df}{d\theta}\).
- Given \(g(x) = \dfrac{1 + x\tan x}{\sin x \sec x}\), find \(\dfrac{dg}{dx}\).
- Given \(h(x) = \dfrac{2 - \cos x \csc x}{(x^2 + 1)\cot x}\), find \(\dfrac{dh}{dx}\).
- Given \(y = 3x\sin x\), find \(y'\) and \(y''\).
- Given \(f(x) = 2\sec x - 5\tan x\), find \(\dfrac{df}{dx}\) and \(\dfrac{d^2f}{dx^2}\).
- Find the equation of the line tangent to the graph of \(g(x) = \sin x\) at \(x = \pi\).
- Find the equation of the line tangent to the graph of \(h(x) = 3\csc x\) at \(x = \dfrac{\pi}{2}\).
- Find the equation of the line tangent to the graph of \(y = \sec x + \tan x\) at \(x = -\dfrac{\pi}{4}\).