Differentiability and the Rules of Differentiation

Name: Differentiability and the Rules of Differentiation
Author: StemPy Lab

Where does a graph have a corner? Define the derivative with limits, see why a differentiable function must be continuous, and then learn the rules: the chain rule, inverse trigonometric, exponential and logarithmic functions, and implicit, logarithmic and parametric differentiation. It covers the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.

3 lessons, about 1 h 15 min3 simulations10 problems4 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Differentiability and the chain rule
The derivative of $f$ at $a$ is the limit of the difference quotient $\dfrac{f(a + h) - f(a)}{h}$ as $h \to 0$ . The function is differentiable at $a$ when this limit exists, which needs the left and right derivatives to be equal. A differentiable function is continuous, but a continuous function can have a corner. The chain rule differentiates a function of a function.
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 2about 25 min
Inverse trigonometric, exponential and logarithmic functions
The derivative of $e^x$ is $e^x$ , and that of $\ln x$ is $\dfrac{1}{x}$ . For another base, $\dfrac{d}{dx}a^x = a^x\ln a$ . The inverse sine, cosine and tangent have derivatives that involve a square root or a sum of squares. Each result combines with the chain rule, and a substitution often simplifies a messy expression before you differentiate.
1 simulation1 practice question1 Python program4 problems
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Lesson 3about 25 min
Implicit, logarithmic and parametric differentiation
When $y$ is hidden inside an equation, differentiate both sides with respect to $x$ and treat $y$ as a function of $x$ . When $x$ appears in the exponent, or in a long product, take logarithms first. When $x$ and $y$ both depend on a parameter $t$ , the slope is $\dfrac{dy/dt}{dx/dt}$ .
1 simulation2 practice questions1 Python program3 problems1 Python lab1 question set1 note
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Differentiability and the Rules of Differentiation: Timed Test

10 questions · 25 min

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Differentiability and the Rules of Differentiation

Course outline (3 lessons)

Differentiability and the chain rule

Inverse trigonometric, exponential and logarithmic functions

Implicit, logarithmic and parametric differentiation

Test Your Learning

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