All in One Place

Everything you need for JC, LC, and college level maths and science classes.

Learn with Ease

We’ve mastered the national curriculum so that you can revise with confidence.

Instant Help

24/7 access to the best tips, walkthroughs, and practice exercises available.

0/1
?
Intros
Lessons
  1. Introduction to Chain Rule
    • "bracket technique" explained!
    exercise: ddxx10\frac{d}{dx}x^{10} VS. ddx(x5+4x36x+8)10\frac{d}{dx}(x^5+4x^3-6x+8)^{10}
0/17
?
Examples
Lessons
  1. Differentiate: Polynomial Functions
    ddx(2x1)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. ddx5sin2x \frac{d}{dx}- \frac{5}{\sin ^2x}
    2. Differentiate: Radical Functions
      1. ddxx3+4x29\frac{d}{dx} \sqrt{x^3+4x^2-9}
      2. ddx3(x2+5)7 \frac{d}{dx} {^3}\sqrt{(x^2+5)^7}
      3. ddx136x4x\frac{d}{dx} \frac{1}{{^3}\sqrt{6x^4-x}}
      4. ddxx+x+x \frac{d}{dx} \sqrt{x+\sqrt{x+\sqrt{x}}}
      5. ddx3lnx \frac{d}{dx} {^3}\sqrt{\ln x}
    3. Differentiate: Trigonometric Functions
      1. Differentiate: y=sin4xy= \sin ^4x
        VS.
        y=sin(x4)y=\sin (x^4)
      2. ddxtan(cose5x2) \frac{d}{dx} \tan (\cos e^{5x^2})
      3. ddθsin(cos(tanθ))\frac{d}{d \theta} \sin (\cos (\tan \theta))
    4. Differentiate: Exponential Functions
      1. ddxetanx\frac{d}{dx} e^{\tan x}
      2. ddxecsc5x2\frac{d}{dx} e^{\csc 5x^2}
      3. ddx2sinx\frac{d}{dx} 2^{\sin x}
      4. ddx52x3\frac{d}{dx} 5^{2^{{x}^3}}
    5. Differentiate: Logarithmic Functions
      1. ddxlnx100 \frac{d}{dx} \ln x^{100}
        VS.
        ddx(lnx)100\frac{d}{dx} (\ln x)^{100}
      2. ddxlog2x3 \frac{d}{dx} \log_{2}{x^3}
    Topic Notes
    ?
    Chain Rule appears everywhere in the world of differential calculus. Whenever we are finding the derivative of a function, be it a composite function or not, we are in fact using the Chain Rule. In this section, we will learn about the concept, the definition and the application of the Chain Rule, as well as a secret trick – "The Bracket Technique".
    Chain Rule
    if: y=  f(              )y = \;f\left( {\;\;\;\;\;\;\;} \right)
    then: dydx=f(              )ddx(                )\frac{{dy}}{{{d}x}} = f'\left( {\;\;\;\;\;\;\;} \right)\cdot\frac{{d}}{{{d}x}}\left( {\;\;\;\;\;\;\;\;} \right)

    Differential Rules
    table of chain rule applications on various functions 1
    table of chain rule applications on various functions 2