Chain rule

Intros
Lessons
1. Introduction to Chain Rule
• "bracket technique" explained!
exercise: $\frac{d}{dx}x^{10}$ VS. $\frac{d}{dx}(x^5+4x^3-6x+8)^{10}$
Examples
Lessons
1. Differentiate: Polynomial Functions
$\frac{d}{dx} (2x-1)^3$
1. Differentiate: Rational Functions
1. $\frac{d}{dx} \frac{1}{(4x^3+7)^{10}}$
2. $\frac{d}{dx}- \frac{5}{\sin ^2x}$
1. $\frac{d}{dx} \sqrt{x^3+4x^2-9}$
2. $\frac{d}{dx} {^3}\sqrt{(x^2+5)^7}$
3. $\frac{d}{dx} \frac{1}{{^3}\sqrt{6x^4-x}}$
4. $\frac{d}{dx} \sqrt{x+\sqrt{x+\sqrt{x}}}$
5. $\frac{d}{dx} {^3}\sqrt{\ln x}$
3. Differentiate: Trigonometric Functions
1. Differentiate: $y= \sin ^4x$
VS.
$y=\sin (x^4)$
2. $\frac{d}{dx} \tan (\cos e^{5x^2})$
3. $\frac{d}{d \theta} \sin (\cos (\tan \theta))$
4. Differentiate: Exponential Functions
1. $\frac{d}{dx} e^{\tan x}$
2. $\frac{d}{dx} e^{\csc 5x^2}$
3. $\frac{d}{dx} 2^{\sin x}$
4. $\frac{d}{dx} 5^{2^{{x}^3}}$
5. Differentiate: Logarithmic Functions
1. $\frac{d}{dx} \ln x^{100}$
VS.
$\frac{d}{dx} (\ln x)^{100}$
2. $\frac{d}{dx} \log_{2}{x^3}$