The chain rule part 2

Presentation

•

Mathematics

•

12th Grade

•

Medium

Sahel Otoom

Used 22+ times

FREE Resource

5 Slides • 8 Questions

Match

Warm Up

Match the following

$\frac{d}{dx}\left(200\right)=$

$\frac{d}{dx}\left(200x\right)=$

$\frac{d}{dx}\left(x^{200}\right)=$

$\frac{d}{dx}\left(\frac{1}{200}x^{200}\right)=$

$\frac{d}{dx}\left(200x^2+200x\right)=$

200

200x¹⁹⁹

x¹⁹⁹

400x+200

Objectives 1.Recall the general power rule and chain rule.
2. Apply the chain rule to real-life UAE-based models (e.g., population, temperature functions).

Match

Match the following

$\frac{d}{dx}\left(20\right)=$

$\frac{d}{dx}\left(20x\right)=$

$\frac{d}{dx}\left(x^{20}\right)=$

$\frac{d}{dx}\left(\frac{1}{20}x^{20}\right)=$

$\frac{d}{dx}\left(20x^2+20x\right)=$

20x¹⁹

x¹⁹

40x+20

Match

Match the following

$\frac{d}{dx}\left(\cos x\right)$

$\frac{d}{dx}\left(\tan x\right)$

$\frac{d}{dx}\left(\sec x\right)$

$\frac{d}{dx}\left(\sin x\right)$

$\frac{d}{dx}\left(\cot x\right)$

- sin x

sec²x

secx tanx

cos x

-csc²x

Multiple Choice

$find\ g'\left(x\right)\ for\ g\left(x\right)=\left(h\left(x\right)\right)^3$

$g'\left(x\right)=3\left(h'\left(x\right)\right)^2$

$g'\left(x\right)=3h'\left(x\right)^2$

$g'\left(x\right)=3\left(h\left(x\right)\right)^2\cdot h'\left(x\right)$

$g'\left(x\right)=3h\left(x\right)^2\cdot h'\left(x\right)$

Multiple Choice

Find $\frac{dr}{d\theta}\ if\ r=\left(\sec\theta+\tan\theta\right)^{-3}$

$-3\left(\sec\theta+\tan\theta\right)^{-4}\cdot\sec\theta$

$-3\left(\sec\theta+\tan\theta\right)^{-4}\left(\sec\theta\tan\theta+\sec^2\theta\right)$

$-3\left(\sec\theta+\tan\theta\right)^{-4}$

$-3\left(\sec\theta\tan\theta+\sec^2\theta\right)^{-4}$

Multiple Choice

$\frac{\text{d}}{\text{d}x}\tan^2\left(3x\right)$

$2\tan\left(3x\right)\sec^2\left(x\right)\cdot3$

$2\tan\left(3x\right)\sec^2\left(3x\right)\cdot3$

$2\sec^2\left(3x\right)$

$2\sec^2\left(3x\right)\cdot3$

Multiple Choice

Given the function $y=\sqrt{5x-7}$ find $\frac{\text{d}x}{\text{d}y}$ .

$\frac{5}{2\sqrt{5x-7}}$

$\frac{1}{2\sqrt{5x-7}}$

$\frac{5}{\sqrt{5x-7}}$

$5\sqrt{5x-7}$

Multiple Choice

$\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}$ Find

$\frac{-5}{\sqrt{10t+12}}\sin\sqrt{10t+12}$

$\frac{-1}{2\sqrt{10t+12}}\sin\sqrt{10t+12}$

$-\sin\sqrt{10t+12}$

$-\sin\left(\frac{5}{\sqrt{10t+12}}\right)$

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