Advertisements
Advertisements
Question
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
Advertisements
Solution
When 0 < x < `pi/4`,cos x > si x
So that cos x – sin x > 0
i.e. f(x) = cos x – sin x
⇒ f′(x) = – sin x – cos x
Hence `"f'"(pi/6) = - sin pi/6 - cos pi/6`
=` 1/2 (1 + sqrt(3))`.
APPEARS IN
RELATED QUESTIONS
if `y = tan^2(log x^3)`, find `(dy)/(dx)`
Find `"dy"/"dx"`If x3 + x2y + xy2 + y3 = 81
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Find the second order derivatives of the following : e2x . tan x
Find `"dy"/"dx"` if, y = (5x3 - 4x2 - 8x)9
Find `"dy"/"dx"` if, y = log(log x)
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
Solve the following:
If y = (6x3 - 3x2 - 9x)10, find `"dy"/"dx"`
Find `"dy"/"dx"`, if y = `2^("x"^"x")`.
If y = x10, then `("d"y)/("d"x)` is ______
If y = x2, then `("d"^2y)/("d"x^2)` is ______
State whether the following statement is True or False:
If x2 + y2 = a2, then `("d"y)/("d"x)` = = 2x + 2y = 2a
y = (6x4 – 5x3 + 2x + 3)6, find `("d"y)/("d"x)`
Solution: Given,
y = (6x4 – 5x3 + 2x + 3)6
Let u = `[6x^4 - 5x^3 + square + 3]`
∴ y = `"u"^square`
∴ `("d"y)/"du"` = 6u6–1
∴ `("d"y)/"du"` = 6( )5
and `"du"/("d"x) = 24x^3 - 15(square) + 2`
By chain rule,
`("d"y)/("d"x) = ("d"y)/square xx square/("d"x)`
∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^square xx (24x^3 - 15x^2 + square)`
If u = x2 + y2 and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = ______
If f(x) = `(x - 2)/(x + 2)`, then f(α x) = ______
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
Derivative of ex sin x w.r.t. e-x cos x is ______.
`"d"/("d"x) [sin(1 - x^2)]^2` = ______.
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
If y = `sec^-1 ((sqrt(x) + 1)/(sqrt(x + 1))) + sin^-1((sqrt(x) - 1)/(sqrt(x) + 1))`, then `"dy"/"dx"` is equal to ______.
y = cos (sin x)
y = `sec (tan sqrt(x))`
y = `cos sqrt(x)`
Let x(t) = `2sqrt(2) cost sqrt(sin2t)` and y(t) = `2sqrt(2) sint sqrt(sin2t), t ∈ (0, π/2)`. Then `(1 + (dy/dx)^2)/((d^2y)/(dx^2)` at t = `π/4` is equal to ______.
Let f(x) = x | x | and g(x) = sin x
Statement I gof is differentiable at x = 0 and its derivative is continuous at that point.
Statement II gof is twice differentiable at x = 0.
If y = 2x2 + a2 + 22 then `dy/dx` = ______.
If `d/dx` [f(x)] = ax+ b and f(0) = 0, then f(x) is equal to ______.
Find `"dy"/"dx" if, e ^(5"x"^2- 2"X"+4)`
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find the rate of change of demand (x) of acommodity with respect to its price (y) if
`y = 12 + 10x + 25x^2`
If y = `root5((3x^2 + 8x +5)^4)`, find `dy/dx`.
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Solve the following.
If `y=root(5)((3x^2 + 8x + 5)^4)`, find `dy/dx`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
If `y = (x + sqrt(a^2 + x^2))^m`, prove that `(a^2 + x^2)(d^2y)/(dx^2) + xdy/dx - m^2y = 0`
