Advertisements
Advertisements
प्रश्न
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a cos θ, y = b cos θ
Advertisements
उत्तर
Given, x = a cos θ and y = b cos θ
Differentiating both sides with respect to θ,
`dx/(dθ)` = −a sin θ
`dy/(dθ)` = −b sin θ
`dy/dx = (dy/(dθ))/(dx/(dθ))`
= `(-b sin θ)/(- a sin θ)`
= `b/a`
APPEARS IN
संबंधित प्रश्न
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 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 + cos 2t) and y = b cos 2t (1 – cos 2t) then find `dy/dx `
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 = (sin^3t)/sqrt(cos 2t), y = (cos^3t)/sqrt(cos 2t)`
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 = `sqrt(a^(sin^(-1)t))`, y = `sqrt(a^(cos^(-1)t))` show that `dy/dx = - y/x`.
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'?
Evaluate : `int (sec^2 x)/(tan^2 x + 4)` dx
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
x = 3cosθ – 2cos3θ, y = 3sinθ – 2sin3θ
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`
If x = t2, y = t3, then `("d"^2"y")/("dx"^2)` is ______.
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)` = ______.
When \(x\) and \(y\) are expressed separately as functions of the same third variable \(t\), which equations are obtained?
In the parametric equations \(x=f(t)\) and \(y=g(t)\), what is \(t\) called?
After writing \(x=f(t)\) and \(y=g(t)\), what should be found separately?
If required, in terms of which variables may the final answer be expressed instead of the parameter?
For \(x=a\cos^3\theta\) and \(y=a\sin^3\theta\), what are \(\frac{dx}{d\theta}\) and \(\frac{dy}{d\theta}\)?
For \(x=a\cos^3\theta\) and \(y=a\sin^3\theta\), what is \(\frac{dy}{dx}\) in terms of \(\theta\)?
If \(x=a\cos t\) and \(y=a\sin t\), what are the derivatives with respect to \(t\)?
If \(x=a\cos t\) and \(y=a\sin t\), what is \(\frac{dy}{dx}\)?
What should always be checked before using the main formula for the derivative of parametric functions?
