Advertisements
Advertisements
प्रश्न
If y = sec (tan−1x) then `("d"y)/("d"x)` at x = 1 is ______.
विकल्प
`1/2`
1
`1/sqrt(2)`
`sqrt(2)`
उत्तर
If y = sec (tan−1x) then `("d"y)/("d"x)` at x = 1 is `bb(1/sqrt(2))`.
Explanation:
[Hint : `"dy"/"dx" = sec(tan^-1x).tan(tan^-1x) xx (1)/(1 + x^2)`
∴ `(dy/dx)_("at" x = 1) = sec(tan^-1 1) xx 1 xx (1)/(1 + 1^2)`
= `sec pi/4 xx (1)/(2) = sqrt(2) xx (1)/(2) = (1)/sqrt(2)]`.
संबंधित प्रश्न
if `y = tan^2(log x^3)`, find `(dy)/(dx)`
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
Solve the following differential equation:
x2 dy + (xy + y2) dx = 0, when x = 1 and y = 1
If y = log (cos ex) then find `"dy"/"dx".`
Find `dy/dx if x + sqrt(xy) + y = 1`
Find `"dy"/"dx"`If x3 + x2y + xy2 + y3 = 81
Find `dy/dx if x^2y^2 - tan^-1(sqrt(x^2 + y^2)) = cot^-1(sqrt(x^2 + y^2))`
Find `"dy"/"dx"` if xey + yex = 1
Find `"dy"/"dx"` if ex+y = cos(x – y)
Find `"dy"/"dx"` if `e^(e^(x - y)) = x/y`
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Find `"dy"/"dx"` if, y = `sqrt("x" + 1/"x")`
Find `"dy"/"dx"` if, y = `root(3)("a"^2 + "x"^2)`
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
Choose the correct alternative.
If y = (5x3 - 4x2 - 8x)9, then `"dy"/"dx"` =
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
Fill in the Blank
If 3x2y + 3xy2 = 0, then `"dy"/"dx"` = ________
Solve the following:
If y = (6x3 - 3x2 - 9x)10, 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.
Find `"dy"/"dx"`, if y = `2^("x"^"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
If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable function of x and `(dx)/(dt)` ≠ 0 then `(dy)/(dx) = ((dy)/(dt))/((dx)/(d"))`.
Hence find `(dy)/(dx)` if x = sin t and y = cost
Choose the correct alternative:
If y = `root(3)((3x^2 + 8x - 6)^5`, then `("d"y)/("d"x)` = ?
If y = x10, then `("d"y)/("d"x)` is ______
If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
If y = x2, then `("d"^2y)/("d"x^2)` is ______
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
`"d"/("d"x) [sin(1 - x^2)]^2` = ______.
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)]
If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
If x = a sec3θ and y = a tan3θ, find `("d"y)/("d"x)` at θ = `pi/3`
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
y = `sec (tan sqrt(x))`
y = `2sqrt(cotx^2)`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
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 ______.
Find `"dy"/"dx" if, e ^(5"x"^2- 2"X"+4)`
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
The differential equation of (x - a)2 + y2 = a2 is ______
Find `dy/dx` if, y = `e^(5 x^2 - 2x + 4)`
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
If f(x) = `sqrt(7*g(x) - 3)`, g(3) = 4 and g'(3) = 5, find f'(3).
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
If x = Φ(t) is a differentiable function of t, then prove that:
`int f(x)dx = int f[Φ(t)]*Φ^'(t)dt`
Hence, find `int(logx)^n/x dx`.
If y = f(u) is a differentiable function of u and u = g(x) is a differentiate function of x such that the composite function y = f[g(x)] is a differentiable function of x then prove that
`dy/dx = dy/(du) xx (du)/dx`
Hence find `dy/dx` if y = log(x2 + 5)
If y = `root5((3x^2 + 8x +5)^4)`, find `dy/dx`.
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
Find `dy/dx` if, `y = e^(5x^2 - 2x +4)`
Solve the following:
If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Solve the following.
If `y=root(5)((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if, `y = e^(5x^2 - 2x + 4)`.
