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Chain rule

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Intros
Lessons
  1. Introduction to Chain Rule
    • "bracket technique" explained!
    • exercise: ddxx10\frac{d}{dx}x^{10} VS. ddx(x5+4x3−6x+8)10\frac{d}{dx}(x^5+4x^3-6x+8)^{10}
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Examples
Lessons
  1. Differentiate: Polynomial Functions
    ddx(2x−1)3 \frac{d}{dx} (2x-1)^3
    1. Differentiate: Rational Functions
      1. ddx1(4x3+7)10 \frac{d}{dx} \frac{1}{(4x^3+7)^{10}}
      2. ddx−5sin⁡2x \frac{d}{dx}- \frac{5}{\sin ^2x}
    2. Differentiate: Radical Functions
      1. ddxx3+4x2−9\frac{d}{dx} \sqrt{x^3+4x^2-9}
      2. ddx3(x2+5)7 \frac{d}{dx} {^3}\sqrt{(x^2+5)^7}
      3. ddx136x4−x\frac{d}{dx} \frac{1}{{^3}\sqrt{6x^4-x}}
      4. ddxx+x+x \frac{d}{dx} \sqrt{x+\sqrt{x+\sqrt{x}}}
      5. ddx3ln⁡x \frac{d}{dx} {^3}\sqrt{\ln x}
    3. Differentiate: Trigonometric Functions
      1. Differentiate: y=sin⁡4xy= \sin ^4x
        VS.
        y=sin⁡(x4)y=\sin (x^4)
      2. ddxtan⁡(cos⁡e5x2) \frac{d}{dx} \tan (\cos e^{5x^2})
      3. ddθsin⁡(cos⁡(tan⁡θ))\frac{d}{d \theta} \sin (\cos (\tan \theta))
    4. Differentiate: Exponential Functions
      1. ddxetan⁡x\frac{d}{dx} e^{\tan x}
      2. ddxecsc⁡5x2\frac{d}{dx} e^{\csc 5x^2}
      3. ddx2sin⁡x\frac{d}{dx} 2^{\sin x}
      4. ddx52x3\frac{d}{dx} 5^{2^{{x}^3}}
    5. Differentiate: Logarithmic Functions
      1. ddxln⁡x100 \frac{d}{dx} \ln x^{100}
        VS.
        ddx(ln⁡x)100\frac{d}{dx} (\ln x)^{100}
      2. ddxlog⁡2x3 \frac{d}{dx} \log_{2}{x^3}