Advertisements
Advertisements
Question
Find `bb(dy/dx)` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
Advertisements
Solution
y = `sin^-1 ((2x)/(1 + x^2))`
Let, x = tan θ
⇒ θ = tan−1 x
∴ `y = sin^-1 ((2 tan theta)/(1 + tan^2 theta))`
= `sin^-1 (sin 2 theta) ... [because sin 2 theta = (2 tan theta)/(1 + tan^2 theta)]`
= 2 θ
y = 2 tan−1 x
∴ `dy/dx = 2 d/dx tan^-1 x`
`dy/dx = 2/(1 + x^2)`
APPEARS IN
RELATED QUESTIONS
Find `bb(dy/dx)` in the following:
2x + 3y = sin x
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
Find `bb(dy/dx)` in the following:
sin2 x + cos2 y = 1
Is |sin x| differentiable? What about cos |x|?
If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`
Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)
Find `"dy"/"dx"`, if : x = `(t + 1/t)^a, y = a^(t+1/t)`, where a > 0, a ≠ 1, t ≠ 0.
Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`
Find `"dy"/"dx"` if : x = a cos3θ, y = a sin3θ at θ = `pi/(3)`
Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`
If y = eax.sin(bx), show that y2 – 2ay1 + (a2 + b2)y = 0.
If 2y = `sqrt(x + 1) + sqrt(x - 1)`, show that 4(x2 – 1)y2 + 4xy1 – y = 0.
Find the nth derivative of the following : (ax + b)m
Find the nth derivative of the following : eax+b
Find the nth derivative of the following : cos (3 – 2x)
Choose the correct option from the given alternatives :
Let `f(1) = 3, f'(1) = -(1)/(3), g(1) = -4 and g'(1) =-(8)/(3).` The derivative of `sqrt([f(x)]^2 + [g(x)]^2` w.r.t. x at x = 1 is
Choose the correct option from the given alternatives :
If f(x) = `sin^-1((4^(x + 1/2))/(1 + 2^(4x)))`, which of the following is not the derivative of f(x)?
Choose the correct option from the given alternatives :
If y = sin (2sin–1 x), then dx = ........
If y `tan^-1(sqrt((a - x)/(a + x)))`, where – a < x < a, then `"dy"/"dx"` = .........
Choose the correct option from the given alternatives :
If y = `a cos (logx) and "A"(d^2y)/(dx^2) + "B""dy"/"dx" + "C"` = 0, then the values of A, B, C are
Differentiate the following w.r.t. x : `sin[2tan^-1(sqrt((1 - x)/(1 + x)))]`
Differentiate the following w.r.t. x : `tan^-1[sqrt((sqrt(1 + x^2) + x)/(sqrt(1 + x^2) - x))]`
If sin y = x sin (a + y), then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.
If x = `e^(x/y)`, then show that `dy/dx = (x - y)/(xlogx)`
Find `"dy"/"dx"` if, x3 + y3 + 4x3y = 0
Choose the correct alternative.
If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?
If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.
If x2 + y2 = t + `1/"t"` and x4 + y4 = t2 + `1/"t"^2` then `("d"y)/("d"x)` = ______
Find `(dy)/(dx)`, if `y = sin^-1 ((2x)/(1 + x^2))`
Find `(d^2y)/(dy^2)`, if y = e4x
If log(x+y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx` if, x = `e^(3t)`, y = `e^sqrtt`
Solve the following.
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
Find `dy/(dx) "if" , x = e^(3t), y = e^sqrtt`.
