Advertisements
Advertisements
Question
Find the derivative of the following function from first principle.
`(x+1)/(x -1)`
Advertisements
Solution
`f(x) = (x + 1)/(x - 1)` and `f(x + h) = (x + h + 1)/(x + h - 1)`
`f(x + h) - f(x) = (x + 1 + h)/(x - 1 + h) - (x + 1)/(x - 1)`
= `((x + 1)(x - 1) + h(x - 1) - (x + 1)(x - 1) - h(x + 1))/((x - 1)(x - 1 + h))`
= `(h(x - 1 - x - 1))/((x - 1)(x - 1 + h))`
= `(-2h)/((x - 1)(x - 1 + h))`
`f'(x) = lim_(h → 0) (f(x + h) - f(x))/h`
= `lim_(h → 0) (-2h)/(h(x - 1)(x - 1 + h))`
= `(-2)/(x - 1)^2`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following function from first principle.
x3 – 27
Find the derivative of the following function from first principle.
(x – 1) (x – 2)
Find the derivative of the following function from first principle.
`1/x^2`
Find the derivative of the following function from first principle:
−x
Find the derivative of the following function from first principle:
(–x)–1
Find the derivative of the following function from first principle:
`cos (x - pi/8)`
Find the equation of tangent and normal to the curve at the given points on it.
y = 3x2 - x + 1 at (1, 3)
Find the equation of tangent and normal to the curve at the given points on it.
2x2 + 3y2 = 5 at (1, 1)
Find the equation of tangent and normal to the curve at the given points on it.
x2 + y2 + xy = 3 at (1, 1)
Find the equations of tangent and normal to the curve y = x2 + 5 where the tangent is parallel to the line 4x − y + 1 = 0.
Find the equations of tangent and normal to the curve y = 3x2 - 3x - 5 where the tangent is parallel to the line 3x − y + 1 = 0.
Choose the correct alternative.
The equation of tangent to the curve y = x2 + 4x + 1 at (-1, -2) is
Choose the correct alternative.
The equation of tangent to the curve x2 + y2 = 5 where the tangent is parallel to the line 2x – y + 1 = 0 are
Choose the correct alternative.
If elasticity of demand η = 1, then demand is
Choose the correct alternative.
If 0 < η < 1, then demand is
Choose the correct alternative.
If f(x) = 3x3 - 9x2 - 27x + 15 then
Fill in the blank:
If f(x) = x - 3x2 + 3x - 100, x ∈ R then f''(x) is ______
State whether the following statement is True or False:
The equation of tangent to the curve y = 4xex at `(-1, (- 4)/"e")` is ye + 4 = 0
Find the equation of tangent and normal to the following curve.
y = x3 - x2 - 1 at the point whose abscissa is -2.
Find the equation of normal to the curve y = `sqrt(x - 3)` which is perpendicular to the line 6x + 3y – 4 = 0.
Choose the correct alternative:
Slope of the normal to the curve 2x2 + 3y2 = 5 at the point (1, 1) on it is
The slope of the tangent to the curve x = `1/"t"`, y = `"t" - 1/"t"`, at t = 2 is ______
Find the equations of tangent and normal to the curve y = 3x2 – x + 1 at the point (1, 3) on it
Find the equation of tangent to the curve y = x2 + 4x at the point whose ordinate is – 3
Find the equation of tangent and normal to the curve y = x2 + 5 where the tangent is parallel to the line 4x – y + 1 = 0.
y = ae2x + be-3x is a solution of D.E. `(d^2y)/dx^2 + dy/dx + by = 0`
Find the equations of tangent and normal to the curve y = 6 - x2 where the normal is parallel to the line x - 4y + 3 = 0
