Advertisements
Advertisements
प्रश्न
Find the derivative of the following function from first principle:
sin (x + 1)
उत्तर
Let f(x) = sin (x + 1)
We have, `d/(dx)` (f(x)) = `lim_(h->0) ([f(x + h) - f(x)])/h`
= `lim_(h->0) (sin (x + h + 1) - sin (x + 1))/h`
= `lim_(h->0)(2 cos ((x + h + 1 + x + 1)/2) sin ((x + h + 1 - x - 1)/2))/h`
= `lim_(h->0)(2[cos ((2(x + 1) + h)/2)sin h/2])/(2 xx (h/2))`
= `lim_(h->0) cos (x + 1 + h/2) ((sin h/2)/ (h/2))`
= `{lim_(h->0) (x + 1 + h/2)} {lim_(h->0) (sin h/2) / (h/2)}`
= cos (x + 1) × (1) = cos (x + 1)
APPEARS IN
संबंधित प्रश्न
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 -1)`
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 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 x2 + y2 = 5 where the tangent is parallel to the line 2x – y + 1 = 0 are
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:
The slope of tangent at any point (a, b) is called as _______.
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
State whether the following statement is True or False:
x + 10y + 21 = 0 is the equation of normal to the curve y = 3x2 + 4x - 5 at (1, 2).
Find the equation of tangent and normal to the following curve.
x = `1/"t", "y" = "t" - 1/"t"`, at t = 2
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
Slope of the tangent to the curve y = 6 – x2 at (2, 2) is ______.
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
