Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"` if x = at2, y = 2at.
उत्तर
x = at2, y = 2at
Differentiating x and y w.r.t. t, we get
`"dx"/"dt" = "d"/"dt"("at"^2) = a"d"/"dt"("t"^2)`
= a x 2t = 2at
and
`"dy"/"dt" = "d"/"dt"(2"at") = 2a"d"/"dt"("t")`
= 2a x 1 = 2a
∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt")`
= `"(2a)/(2at)`
= `(1)/"t"`
APPEARS IN
संबंधित प्रश्न
Find `dy/dx` in the following:
2x + 3y = sin x
Find `dy/dx` in the following:
ax + by2 = cos y
Find `dx/dy` in the following.
x2 + xy + y2 = 100
Find `dy/dx` in the following:
sin2 y + cos xy = k
Find `dy/dx` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
if `x^y + y^x = a^b`then Find `dy/dx`
Show that the derivative of the function f given by
If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]
, find f'(4).
Examine the differentialibilty of the function f defined by
\[f\left( x \right) = \begin{cases}2x + 3 & \text { if }- 3 \leq x \leq - 2 \\ \begin{array}xx + 1 \\ x + 2\end{array} & \begin{array} i\text { if } - 2 \leq x < 0 \\\text { if } 0 \leq x \leq 1\end{array}\end{cases}\]
Is |sin x| differentiable? What about cos |x|?
If f (x) = |x − 2| write whether f' (2) exists or not.
Differentiate e4x + 5 w.r..t.e3x
Differentiate tan-1 (cot 2x) w.r.t.x.
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
Discuss extreme values of the function f(x) = x.logx
Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ
Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
Find `"dy"/"dx"`, if : `x = cos^-1(4t^3 - 3t), y = tan^-1(sqrt(1 - t^2)/t)`.
Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`
Find `"dy"/"dx"` if : x = a cos3θ, y = a sin3θ at θ = `pi/(3)`
Find `"dy"/"dx"` if : x = t2 + t + 1, y = `sin((pit)/2) + cos((pit)/2) "at" t = 1`
DIfferentiate x sin x w.r.t. tan x.
Find `(d^2y)/(dx^2)` of the following : x = a(θ – sin θ), y = a(1 – cos θ)
Find `(d^2y)/(dx^2)` of the following : x = a cos θ, y = b sin θ at θ = `π/4`.
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
If x2 + 6xy + y2 = 10, show that `(d^2y)/(dx^2) = (80)/(3x + y)^3`.
Find the nth derivative of the following : (ax + b)m
Find the nth derivative of the following : apx+q
Find the nth derivative of the following : cos x
Find the nth derivative of the following : `(1)/(3x - 5)`
Choose the correct option from the given alternatives :
Let `f(1) = 3, f'(1) = -(1)/(3), g(1) = -4 and g'(1) =-(8)/(3).` The derivative of `sqrt([f(x)]^2 + [g(x)]^2` w.r.t. x at x = 1 is
Choose the correct option from the given alternatives :
If f(x) = `sin^-1((4^(x + 1/2))/(1 + 2^(4x)))`, which of the following is not the derivative of f(x)?
Choose the correct option from the given alternatives :
If y = sin (2sin–1 x), then dx = ........
Choose the correct option from the given alternatives :
If y = `tan^-1(x/(1 + sqrt(1 - x^2))) + sin[2tan^-1(sqrt((1 - x)/(1 + x)))] "then" "dy"/"dx"` = ...........
If y `tan^-1(sqrt((a - x)/(a + x)))`, where – a < x < a, then `"dy"/"dx"` = .........
Choose the correct option from the given alternatives :
If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........
Choose the correct option from the given alternatives :
If y = `a cos (logx) and "A"(d^2y)/(dx^2) + "B""dy"/"dx" + "C"` = 0, then the values of A, B, C are
Differentiate the following w.r.t. x : `sin^2[cot^-1(sqrt((1 + x)/(1 - x)))]`
If x sin (a + y) + sin a . cos (a + y) = 0, then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If `x = e^(x/y)`, then show that `"dy"/"dx" = (x - y)/(xlogx)`
Differentiate log `[(sqrt(1 + x^2) + x)/(sqrt(1 + x^2 - x)]]` w.r.t. cos (log x).
If log y = log (sin x) – x2, show that `(d^2y)/(dx^2) + 4x "dy"/"dx" + (4x^2 + 3)y` = 0.
If x= a cos θ, y = b sin θ, show that `a^2[y(d^2y)/(dx^2) + (dy/dx)^2] + b^2` = 0.
Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`
Find `"dy"/"dx"` if, xy = log (xy)
If log (x + y) = log (xy) + a then show that, `"dy"/"dx" = (- "y"^2)/"x"^2`.
Choose the correct alternative.
If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?
State whether the following is True or False:
The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`
If x2 + y2 = t + `1/"t"` and x4 + y4 = t2 + `1/"t"^2` then `("d"y)/("d"x)` = ______
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt("a"))`
`(dy)/(dx)` of `2x + 3y = sin x` is:-
Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`
y = `e^(x3)`
If y = y(x) is an implicit function of x such that loge(x + y) = 4xy, then `(d^2y)/(dx^2)` at x = 0 is equal to ______.
If y = `sqrt(tan x + sqrt(tanx + sqrt(tanx + .... + ∞)`, then show that `dy/dx = (sec^2x)/(2y - 1)`.
Find `dy/dx` at x = 0.
Find `dy/dx if, x= e^(3t), y = e^sqrtt`
If log(x+y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx` if, x = `e^(3t)`, y = `e^sqrtt`
If log (x + y) = log (xy) + a then show that, `dy/dx = (−y^2)/x^ 2`
If log (x+y) = log (xy) + a then show that, `dy/dx= (-y^2)/(x^2)`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
