Advertisements
Advertisements
प्रश्न
If x=at2, y= 2at , then find dy/dx.
उत्तर
We have, `y = 2at `
`dy/dt=2ad/dt(t)=2a(1)=2a`
also `x=at^2`
`dx/dx=a d/dt(t^2)=a(2t)=2at`
now `dy/dx= (dy/dt)/(dx/dt)=(2a)/(2at)=1/t`
APPEARS IN
संबंधित प्रश्न
find dy/dx if x=e2t , y=`e^sqrtt`
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 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 = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t) then find `dy/dx `
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx`
`x = 2at^2, y = at^4`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = sin t, y = cos 2t
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
`x = 4t, y = 4/y`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
`x = a(cos t + log tan t/2), y = a sin t`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ)
If `x = acos^3t`, `y = asin^3 t`,
Show that `(dy)/(dx) =- (y/x)^(1/3)`
If X = f(t) and Y = g(t) Are Differentiable Functions of t , then prove that y is a differentiable function of x and
`"dy"/"dx" =("dy"/"dt")/("dx"/"dt" ) , "where" "dx"/"dt" ≠ 0`
Hence find `"dy"/"dx"` if x = a cos2 t and y = a sin2 t.
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'?
Evaluate : `int (sec^2 x)/(tan^2 x + 4)` dx
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
x = `"e"^theta (theta + 1/theta)`, y= `"e"^-theta (theta - 1/theta)`
x = 3cosθ – 2cos3θ, y = 3sinθ – 2sin3θ
sin x = `(2"t")/(1 + "t"^2)`, tan y = `(2"t")/(1 - "t"^2)`
If x = ecos2t and y = esin2t, prove that `"dy"/"dx" = (-y log x)/(xlogy)`
If x = 3sint – sin 3t, y = 3cost – cos 3t, find `"dy"/"dx"` at t = `pi/3`
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 ____________.
Form the point of intersection (P) of lines given by x2 – y2 – 2x + 2y = 0, points A, B, C, Dare taken on the lines at a distance of `2sqrt(2)` units to form a quadrilateral whose area is A1 and the area of the quadrilateral formed by joining the circumcentres of ΔPAB, ΔPBC, ΔPCD, ΔPDA is A2, then `A_1/A_2` equals
If x = `a[cosθ + logtan θ/2]`, y = asinθ then `(dy)/(dx)` = ______.
