Advertisements
Advertisements
प्रश्न
Find the derivative of the following w. r. t. x by using method of first principle:
x2 + 3x – 1
Advertisements
उत्तर
Let f(x) = x2 + 3x – 1
∴ f(x + h) = (x + h)2 + 3(x + h) – 1
= x2 + 2xh + h2 + 3x + 3h – 1
By first principle, we get
f'(x) = `lim_("h" -> 0) ("f"(x + "h") - "f"(x))/"h"`
= `lim_("h" -> 0) ([x^2 + 2x"h" + "h"^2 + 3x + 3"h" - 1] - [x^2 + 3x - 1])/"h"`
= `lim_("h" -> 0) (2x"h" + "h"^2 + 3"h")/"h"`
= `lim_("h" -> 0) ("h"(2x + "h" + 3))/"h"`
= `lim_("h" -> 0) (2x + "h" + 3)` ...[∵ h → 0, ∴ h ≠ 0]
= 2x + 3
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following function w.r.t. x.:
x–9
Differentiate the following w. r. t. x.: x5 + 3x4
Differentiate the following w. r. t. x. : `x sqrtx + logx − e^x`
Differentiate the following w. r. t. x. : `x^(5/2) + 5x^(7/5)`
Differentiate the following w. r. t. x. : ex log x
Differentiate the following w. r. t. x. : x3 .3x
Find the derivative of the following w. r. t. x by using method of first principle:
sin (3x)
Find the derivative of the following w. r. t. x by using method of first principle:
e2x+1
Find the derivative of the following w. r. t. x by using method of first principle:
3x
Find the derivative of the following w. r. t. x by using method of first principle:
log (2x + 5)
Find the derivative of the following w. r. t. x by using method of first principle:
tan (2x + 3)
Find the derivative of the following w. r. t. x by using method of first principle:
sec (5x − 2)
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
`sqrt(2x + 5)` at x = 2
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
tan x at x = `pi/4`
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
`"e"^(3x - 4)` at x = 2
Show that f(x) = x2 is continuous and differentiable at x = 0
Discuss the continuity and differentiability of f(x) = (2x + 3) |2x + 3| at x = `- 3/2`
Discuss the continuity and differentiability of f(x) at x = 2
f(x) = [x] if x ∈ [0, 4). [where [*] is a greatest integer (floor) function]
Test the continuity and differentiability of f(x) `{:(= 3 x + 2, "if" x > 2),(= 12 - x^2, "if" x ≤ 2):}}` at x = 2
If f(x) `{:(= sin x - cos x, "if" x ≤ pi/2),(= 2x - pi + 1, "if" x > pi /2):}` Test the continuity and differentiability of f at x = `π/2`
Select the correct answer from the given alternative:
If, f(x) = `x^50/50 + x^49/49 + x^48/48 + .... +x^2/2 + x + 1`, thef f'(1) =
Determine whether the following function is differentiable at x = 3 where,
f(x) `{:(= x^2 + 2"," , "for" x ≥ 3),(= 6x - 7"," , "for" x < 3):}`
Find the values of p and q that make function f(x) differentiable everywhere on R
f(x) `{:( = 3 - x"," , "for" x < 1),(= "p"x^2 + "q"x",", "for" x ≥ 1):}`
Determine the values of p and q that make the function f(x) differentiable on R where
f(x) `{:( = "p"x^3",", "for" x < 2),(= x^2 + "q"",", "for" x ≥ 2):}`
Determine all real values of p and q that ensure the function
f(x) `{:( = "p"x + "q"",", "for" x ≤ 1),(= tan ((pix)/4)",", "for" 1 < x < 2):}` is differentiable at x = 1
Test whether the function f(x) `{:(= 5x - 3x^2",", "for" x ≥ 1),(= 3 - x",", "for" x < 1):}` is differentiable at x = 1
If y = `"e"^x/sqrt(x)` find `("d"y)/("d"x)` when x = 1
