Advertisements
Advertisements
प्रश्न
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
Advertisements
उत्तर
Given that,
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
Differentiating both the given parametric functions w.r.t. t
`"dx"/"dt" = 1 - 1/"t"^2`, `"dy"/"dt" = 1 + 1/"t"^2`
∴ `"dy"/"dx" = (("dy")/("dt"))/(("dx")/("dt"))`
= `(1 + 1/"t"^2)/(1 - 1/"t"^2)`
= `("t"^2 + 1)/("t"^2 - 1)`
Hence, `"dy"/"dx" = ("t"^2 + 1)/("t"^2 - 1)`.
APPEARS IN
संबंधित प्रश्न
If `log_10((x^3-y^3)/(x^3+y^3))=2 "then show that" dy/dx = [-99x^2]/[101y^2]`
find dy/dx if x=e2t , y=`e^sqrtt`
If x = f(t), y = g(t) are differentiable functions of parammeter ‘ t ’ then prove that y is a differentiable function of 'x' and hence, find dy/dx if x=a cost, y=a sint
If x=at2, y= 2at , then find dy/dx.
If `x=a(t-1/t),y=a(t+1/t)`, then show that `dy/dx=x/y`
If `ax^2+2hxy+by^2=0` , show that `(d^2y)/(dx^2)=0`
If y =1 − cos θ, x = 1 − sin θ, then `dy/dx "at" θ =pi/4` is ______
If x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), find `dy/dx `
If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`
If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of `dy/dx `at t = `pi/4`
If x = cos t (3 – 2 cos2 t) and y = sin t (3 – 2 sin2 t), find the value of dx/dy at t =4/π.
Derivatives of tan3θ with respect to sec3θ at θ=π/3 is
(A)` 3/2`
(B) `sqrt3/2`
(C) `1/2`
(D) `-sqrt3/2`
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = 2at2, y = at4
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = cos θ – cos 2θ, y = sin θ – sin 2θ
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a (θ – sin θ), y = a (1 + cos θ)
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = `a(cos t + log tan t/2)`, y = a sin t
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a sec θ, y = b tan θ
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)
If x = `sqrt(a^(sin^(-1)t))`, y = `sqrt(a^(cos^(-1)t))` show that `dy/dx = - y/x`.
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`
IF `y = e^(sin-1x) and z =e^(-cos-1x),` prove that `dy/dz = e^x//2`
The cost C of producing x articles is given as C = x3-16x2 + 47x. For what values of x, with the average cost is decreasing'?
If y = sin -1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`
x = `"e"^theta (theta + 1/theta)`, y= `"e"^-theta (theta - 1/theta)`
If x = 3sint – sin 3t, y = 3cost – cos 3t, find `"dy"/"dx"` at t = `pi/3`
If x = t2, y = t3, then `("d"^2"y")/("dx"^2)` is ______.
Derivative of x2 w.r.t. x3 is ______.
If y `= "Ae"^(5"x") + "Be"^(-5"x") "x" "then" ("d"^2 "y")/"dx"^2` is equal to ____________.
If x = `a[cosθ + logtan θ/2]`, y = asinθ then `(dy)/(dx)` = ______.
Let a function y = f(x) is defined by x = eθsinθ and y = θesinθ, where θ is a real parameter, then value of `lim_(θ→0)`f'(x) is ______.
