LECTURE-3
DIFFERENTIAL CALCULUS,
GEOMETRICAL & PHYSICAL
MEANING OF DERIVATIVES
& RULES OF
DIFFERENTIATION
1
,Let us consider a curve and we find out the slope of the tangent
line to the curve at P(1, 1).
First Method
1. Draw the graph of
2. Draw a tangent line to the curve at the point P(1, 1).
y
Q (x2, y2)
2
,3. Take another point on this line and find the slope of this
tangent line by using the formula:
Slope of the tangent line to the curve is the derivative of the
function. This method gives an approximate answer (because
of the inaccuracy of drawing the tangent) and it is also so very
time consuming.
3
, Second Method
Consider two points on the curve
𝑄 ( 𝑥 +h , 𝑓 ( 𝑥 +h ) )
𝑃 ( 𝑥 , 𝑓 ( 𝑥 ))
h
𝑥 𝑥+ h
4
DIFFERENTIAL CALCULUS,
GEOMETRICAL & PHYSICAL
MEANING OF DERIVATIVES
& RULES OF
DIFFERENTIATION
1
,Let us consider a curve and we find out the slope of the tangent
line to the curve at P(1, 1).
First Method
1. Draw the graph of
2. Draw a tangent line to the curve at the point P(1, 1).
y
Q (x2, y2)
2
,3. Take another point on this line and find the slope of this
tangent line by using the formula:
Slope of the tangent line to the curve is the derivative of the
function. This method gives an approximate answer (because
of the inaccuracy of drawing the tangent) and it is also so very
time consuming.
3
, Second Method
Consider two points on the curve
𝑄 ( 𝑥 +h , 𝑓 ( 𝑥 +h ) )
𝑃 ( 𝑥 , 𝑓 ( 𝑥 ))
h
𝑥 𝑥+ h
4
