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What does the Differentiation revision sheet cover?

Rate of change, and the definition of the derivative, Left-hand and right-hand derivatives, Worked: derivative of the square root, from first principle, Worked: derivative of sin x at a named point, Derivatives of standard functions, from first principle, Differentiability and continuity, Worked: |x| is continuous but not differentiable at 0, Sum, difference and constant-multiple rules, sum, difference, constant multiple, for any real k, Where the product rule comes from.

Is this for Class 11 Maharashtra HSC Mathematics?

Yes, it is written for the Maharashtra HSC Mathematics syllabus.

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Differentiation — Class 11 Maharashtra HSC Mathematics revision notes

A 5-page visual revision sheet for Differentiation, written for Class 11 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

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Differentiation in one look

the rate of change at a single instant, built from a limit of a limiting ratio

Rate of change, and the definition of the derivative

average speed is total distance over time taken
the SPEED AT AN INSTANT is the limit of that ratio as the time shrinks to zero
for f defined near a, if lim_hto0f(a+h)-f(a)/h exists
then f is differentiable at a, and this limit is f'(a)
the process of finding a derivative is called differentiation; for a general x, f'(x)=dy/dx where y=f(x)

Left-hand and right-hand derivatives

left-hand derivative at a: Lf'(a)=lim_hto0^-f(a+h)-f(a)/h
right-hand derivative at a: Rf'(a)=lim_hto0^+f(a+h)-f(a)/h
f is differentiable at a exactly when Lf'(a)=Rf'(a); that common value is f'(a)

Worked: derivative of the square root, from first principle

Q. find the derivative of f(x)=√x using the first-principle definition

f'(x)=lim_hto0frac√x+h-√xh
multiply top and bottom by the conjugate √x+h+√x: the numerator becomes (x+h)-x=h
frachh(√x+h+√x)=frac1√x+h+√x, valid since h≠0 as the limit is approached
let hto0: frac1√x+√x

Answer: f'(x)=frac12√x

Page 1 of 5. The full sheet, all 5 pages, opens free in the app.

What this Differentiation sheet covers

Rate of change, and the definition of the derivative
Left-hand and right-hand derivatives
Worked: derivative of the square root, from first principle
Worked: derivative of sin x at a named point
Derivatives of standard functions, from first principle
Differentiability and continuity
Worked: |x| is continuous but not differentiable at 0
Sum, difference and constant-multiple rules
sum
difference
constant multiple, for any real k
Where the product rule comes from
Product and quotient rules
product rule
quotient rule, v≠0
Worked: differentiating a sum of three shapes
Worked: the quotient rule on an exponential ratio
Implicit and Parametric Forms
Implicit, F(x,y)=0
Parametric, x=f(t), y=g(t)
Worked: continuous but not differentiable at a joint
Reading the chapter together
Symbols
Traps that cost marks
Tricks that save time

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