3.5: The Chain Rule

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Feb 27, 2024
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- 3.4: Derivatives of Trigonometric Functions
- 3.6: Derivatives as Rates of Change

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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 $x = 2$ .

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