Advertisements
Advertisements
Question
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
Advertisements
Solution
Put x = tan θ
Where `(-pi)/6 < θ < pi/6`
Therefore, y = `tan^-1 ((3tan theta - tan^3theta)/(1 - 3 tan^2theta))`
= `tan^-1 (tan 3theta)`
= 3θ ...`(because (-pi)/2 < 3theta < pi/2)`
= 3tan–1x
Hence, `("d"y)/("d"x) = 3/(1 + x^2)`
APPEARS IN
RELATED QUESTIONS
Solve the following differential equation:
x2 dy + (xy + y2) dx = 0, when x = 1 and y = 1
Find `"dy"/"dx"` if ex+y = cos(x – y)
Find `"dy"/"dx"` if cos (xy) = x + y
Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`
Find the second order derivatives of the following : xx
Find `dy/dx` if, y = `sqrt(x + 1/x)`
Find `"dy"/"dx"` if, y = (5x3 - 4x2 - 8x)9
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
Fill in the Blank.
If 3x2y + 3xy2 = 0, then `(dy)/(dx)` = ______.
`d/dx(10^x) = x*10^(x - 1)`
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
If x = cos−1(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______
If x = f(t) and y = g(t) are differentiable functions of t so that y is a differentiable function of x and `(dx)/(dt)` ≠ 0 then `(dy)/(dx) = ((dy)/(dt))/((dx)/(d"))`.
Hence find `(dy)/(dx)` if x = sin t and y = cost
Differentiate `sqrt(tansqrt(x))` w.r.t. x
If `sqrt(1 - x^2) + sqrt(1 - y^2) = a(x - y)`, prove that `(dy)/(dx) = sqrt((1 - y^2)/(1 - x^2))`.
Differentiate the function from over no 15 to 20 sin (x2 + 5)
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
If f(x) = `{{:(x^3 + 1",", x < 0),(x^2 + 1",", x ≥ 0):}`, g(x) = `{{:((x - 1)^(1//3)",", x < 1),((x - 1)^(1//2)",", x ≥ 1):}`, then (gof) (x) is equal to ______.
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
Find `"dy"/"dx"` if, `"y" = "e"^(5"x"^2 - 2"x" + 4)`
Find `dy/dx` if, y = `e^(5 x^2 - 2x + 4)`
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find the rate of change of demand (x) of acommodity with respect to its price (y) if
`y = 12 + 10x + 25x^2`
If f(x) = `sqrt(7*g(x) - 3)`, g(3) = 4 and g'(3) = 5, find f'(3).
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`
Solve the following:
If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
