Advertisements
Advertisements
Question
find dy/dx if x=e2t , y=`e^sqrtt`
Solution
x=e2t , y=`e^sqrtt`
Differentiating x w.r.t t
`"dx"/"dt"=d(e^(2t))/(dt)=e^(2t)d/"dt"(2t)=2e^(2t)`
Differentiating y w.r.t t
`"dy"/"dt"=d(e^(sqrt t))/(dt)=e^(sqrt t)d/"dt"(sqrt t)=(e^(sqrt t))/(2sqrt t)`
By parametric rule we get
`dy/dx=("dy"/"dt")/("dx"/"dt")`
`=((e^(sqrt t))/(2sqrt t))/(2e^(2t))`
`=(e^sqrtt)/(4sqrt t.e^(2t))`
`e^sqrtt`
APPEARS IN
RELATED QUESTIONS
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 `ax^2+2hxy+by^2=0` , show that `(d^2y)/(dx^2)=0`
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 `
Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`
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 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 = a cos θ, y = b cos θ
If x and y are connected parametrically by the equation without eliminating the parameter, find `dy/dx`.
x = cos θ – cos 2θ, y = sin θ – sin 2θ
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a (θ – sin θ), y = a (1 + cos θ)
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
`x = (sin^3t)/sqrt(cos 2t), y = (cos^3t)/sqrt(cos 2t)`
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)
Evaluate : `int (sec^2 x)/(tan^2 x + 4)` dx
Differentiate `x/sinx` w.r.t. sin x
If x = t2, y = t3, then `("d"^2"y")/("dx"^2)` is ______.
Derivative of x2 w.r.t. x3 is ______.
If `"x = a sin" theta "and y = b cos" theta, "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
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 ______.
