3.4: Derivatives of Trigonometric Functions
- Page ID
- 143972
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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 \(x = -\dfrac{\pi}{4}\).