Advertisements
Advertisements
प्रश्न
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
Advertisements
उत्तर
x = tan-1t and y = t3
∴ `(dx)/(dt) = 1/(1 + t^2) "and" (dy)/(dt) = 3t^2`
∴ `(dy)/(dx) = ((dy/dt))/((dx/dt)) = (3t^2)/(1/(1 + t^2))`
⇒ `(dy)/(dx) = 3t^2(1 + t^2)`
APPEARS IN
संबंधित प्रश्न
Find `bb(dy/dx)` in the following:
x2 + xy + y2 = 100
Is |sin x| differentiable? What about cos |x|?
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Find `dy/dx if x^3 + y^2 + xy = 7`
Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`
Discuss extreme values of the function f(x) = x.logx
Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`
Differentiate `cos^-1((1 - x^2)/(1 + x^2)) w.r.t. tan^-1 x.`
Find `(d^2y)/(dx^2)` of the following : x = a(θ – sin θ), y = a(1 – cos θ)
If 2y = `sqrt(x + 1) + sqrt(x - 1)`, show that 4(x2 – 1)y2 + 4xy1 – y = 0.
Choose the correct option from the given alternatives :
If `xsqrt(y + 1) + ysqrt(x + 1) = 0 and x ≠ y, "then" "dy"/"dx"` = ........
Differentiate the following w.r.t. x : `sin^2[cot^-1(sqrt((1 + x)/(1 - x)))]`
Choose the correct alternative.
If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?`
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
y = `e^(x3)`
If `tan ((x + y)/(x - y))` = k, then `dy/dx` is equal to ______.
If log(x+y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
