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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← Continuity and Differentiability

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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

Your teacher

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