Advertisements
Advertisements
प्रश्न
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a sec θ, y = b tan θ
उत्तर
Given, x = a sec θ and y = b tan θ.
Differentiating both sides with respect to θ,
`dx/(d theta) = a sec θ tan θ ` and `dy/(d theta) = b sec^2 θ`
`therefore dy/dx = (dy/(d theta))/(dx/(d theta))`
`= (b sec^2 theta)/(a sec theta tan theta) = (b sec theta)/(a tan theta)`
`= b/a sec theta cot theta`
`= b/a xx 1/(cos theta) * (cos theta)/(sin theta)`
`= b/a xx 1/(sin theta)`
`= b/a cosec theta`
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 x=a sin 2t(1+cos 2t) and y=b cos 2t(1−cos 2t), 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)`
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.
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 = 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 (θ – sin θ), y = a (1 + cos θ)
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/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)`
x = `(1 + log "t")/"t"^2`, y = `(3 + 2 log "t")/"t"`
If x = ecos2t and y = esin2t, prove that `"dy"/"dx" = (-y log x)/(xlogy)`
If x = asin2t (1 + cos2t) and y = b cos2t (1–cos2t), show that `("dy"/"dx")_("at t" = pi/4) = "b"/"a"`
If x = 3sint – sin 3t, y = 3cost – cos 3t, find `"dy"/"dx"` at t = `pi/3`
Differentiate `tan^-1 ((sqrt(1 + x^2) - 1)/x)` w.r.t. tan–1x, when x ≠ 0
If x = sint and y = sin pt, prove that `(1 - x^2) ("d"^2"y")/("dx"^2) - x "dy"/"dx" + "p"^2y` = 0
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 ____________.
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)` = ______.
