3.5: The Chain Rule
- Page ID
- 144104
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- Given \(f(x) = (x + 1)^{100}\), find \(f'(x)\).
- Given \(y = (7x^2 - 12x + 3)^5\), find \(y'\).
- Given \(g(x) = \sin x^2\), find \(g'(x)\).
- Given \(h(x) = \sin^2 x\), find \(h'(x)\).
- Given \(F(x) = \sqrt{1 - x^2}\), find \(\dfrac{dF}{dx}\).
- Given \(y = \sqrt{3x^2 + 2x - 4}\), find \(y'\).
- Given \(f(x) = \sec(\tan x)\), find \(\dfrac{df}{dx}\).
- Given \(g(x) = \left(2x^3 - \dfrac{1}{x}\right)^{-3}\), find \(\dfrac{dg}{dx}\).
- Given \(h(x) = \dfrac{1}{(5x - 3x^5)^4}\), find \(\dfrac{dh}{dx}\).
- Given \(y = \sqrt{1 + \sqrt{x}}\), find \(\dfrac{dy}{dx}\).
- Given \(f(x) = \cos \sqrt{x}\), find \(f'(x)\).
- Given \(g(x) = \sin(\cos 2x)\), find \(g'(x)\).
- Given \(h(x) = \Bigl(\csc(3x - 2) + \cot(3x - 2)\Bigr)^5\), find \(h'(x)\).
- Given \(y = \tan^2 \left(\dfrac{1}{x}\right)\), find \(y'\).
- Given \(f(x) = \dfrac{1}{\sqrt{\sec x}}\), find \(\dfrac{df}{dx}\).
- Given \(g(x) = \sin(x^2\csc x)\), find \(\dfrac{dg}{dx}\).
- Given \(h(x) = \cos\left(\dfrac{x}{1 + x}\right)\), find \(\dfrac{dh}{dx}\).
- Given \(y = \tan(x^2 + x)\cot(2x - 3)\), find \(\dfrac{dy}{dx}\).
- Given \(f(x) = \dfrac{\sin (2x^3)}{1 - \cos(3x + 4)}\), find \(f'(x)\).
- Given \(g(x) = \sqrt{2x^3 - \cos^2(4x)}\), find \(g'(x)\).
- Given \(h(x) = \sec^5 \left(\sqrt{5x^2 - 4}\right)\), find \(h'(x)\).
- Given \(y(x) = \sin(x^2)\), find \(y''(x)\).
- Given \(f(x) = \tan^2 x\), find \(\dfrac{d^2f}{dx^2}\).
- Find the equation of the line tangent to the graph of \(y = \sqrt{2x^3 - 4x}\) at \(x = 2\).