3.4: Derivatives of Trigonometric Functions

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Dec 20, 2023
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- 3.3: Differentiation Rules
- 3.5: The Chain Rule

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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 $x = -\dfrac{\pi}{4}$ .

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