Advertisements
Advertisements
प्रश्न
If f(x) = |cos x|, find f'`((3pi)/4)`
उत्तर
When `pi/2` < x , pi, cos x < 0`
So that |cos x| = `- cos x`
i.e., f(x) = `- cos x`
⇒ f'(x) = sin x.
Hence, `"f'"((3pi)/4) = sin ((3pi)/4) = 1/sqrt(2)`
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"` if cos (xy) = x + y
Find the second order derivatives of the following : e4x. cos 5x
Fill in the Blank
If 3x2y + 3xy2 = 0, then `"dy"/"dx"` = ________
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`.
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x – x2.
Differentiate `"e"^("4x" + 5)` with respect to 104x.
If y = sec (tan−1x) then `("d"y)/("d"x)` at x = 1 is ______.
If sin−1(x3 + y3) = a then `("d"y)/("d"x)` = ______
If y = cos−1 [sin (4x)], find `("d"y)/("d"x)`
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
Choose the correct alternative:
If y = `x^(sqrt(x))`, then `("d"y)/("d"x)` = ?
State whether the following statement is True or False:
If x2 + y2 = a2, then `("d"y)/("d"x)` = = 2x + 2y = 2a
Find `("d"y)/("d"x)`, if y = `root(5)((3x^2 + 8x + 5)^4`
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 y = `2/(sqrt(a^2 - b^2))tan^-1[sqrt((a - b)/(a + b)) tan x/2], "then" (d^2y)/dx^2|_{x = pi/2}` = ______
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
Derivative of ex sin x w.r.t. e-x cos x is ______.
If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.
Given f(x) = `1/(x - 1)`. Find the points of discontinuity of the composite function y = f[f(x)]
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.
Solve the following:
If`y=root(5)((3x^2+8x+5)^4),"find" (dy)/dx`
The differential equation of (x - a)2 + y2 = a2 is ______
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
Find `dy/(dx)` if, y = `e^(5x^2 - 2x + 4)`