Advertisements
Advertisements
प्रश्न
If `tan ((x + y)/(x - y))` = k, then `dy/dx` is equal to ______.
विकल्प
`(-y)/x`
`y/x`
`sec^2 (y/x)`
`-sec^2 (y/x)`
Advertisements
उत्तर
If `tan ((x + y)/(x - y))` = k, then `dy/dx` is equal to `underlinebb(y/x)`.
Explanation:
Given
`tan((x + y)/(x - y))` = k
`(x + y)/(x - y)` = tan–1 k
On differentiating both sides, w.r.t. x, we get
`((x - y)d/dx(x + y) - (x + y)d/dx(x - y))/(x - y)^2 = d/dx [tan^-1 k]`
`\implies ((x - y)(1 + dy/dx) - (x + y)(1 - dy/dx))/(x - y)^2` = 0
`\implies (x - y)(1 + dy/dx) - (x + y)(1 - dy/dx)` = 0
`\implies (x - y) + (x - y) dy/dx = (x + y) - (x + y) dy/dx`
`\implies [(x - y) + (x + y)] dy/dx` = (x + y) – (x – y)
`\implies 2x dy/dx` = 2y
`\implies dy/dx = y/x`.
APPEARS IN
संबंधित प्रश्न
If y=eax ,show that `xdy/dx=ylogy`
If xpyq = (x + y)p+q then Prove that `dy/dx = y/x`
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
Find `bb(dy/dx)` in the following:
xy + y2 = tan x + y
Find `bb(dy/dx)` in the following:
x2 + xy + y2 = 100
Find `bb(dy/dx)` in the following:
sin2 y + cos xy = k
Find `bb(dy/dx)` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Differentiate e4x + 5 w.r..t.e3x
Find `(dy)/(dx) if y = cos^-1 (√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 cos3θ, y = a sin3θ at θ = `pi/(3)`
Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`
Differentiate xx w.r.t. xsix.
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
If 2y = `sqrt(x + 1) + sqrt(x - 1)`, show that 4(x2 – 1)y2 + 4xy1 – y = 0.
If x = a sin t – b cos t, y = a cos t + b sin t, show that `(d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)`.
Choose the correct option from the given alternatives :
If `xsqrt(y + 1) + ysqrt(x + 1) = 0 and x ≠ y, "then" "dy"/"dx"` = ........
Solve the following :
f(x) = –x, for – 2 ≤ x < 0
= 2x, for 0 ≤ x < 2
= `(18 - x)/(4)`, for 2 < x ≤ 7
g(x) = 6 – 3x, for 0 ≤ x < 2
= `(2x - 4)/(3)`, for 2 < x ≤ 7
Let u (x) = f[g(x)], v(x) = g[f(x)] and w(x) = g[g(x)]. Find each derivative at x = 1, if it exists i.e. find u'(1), v' (1) and w'(1). If it doesn't exist, then explain why?
If `xsqrt(1 - y^2) + ysqrt(1 - x^2)` = 1, then show that `"dy"/"dx" = -sqrt((1 - y^2)/(1 - x^2)`.
If y2 = a2cos2x + b2sin2x, show that `y + (d^2y)/(dx^2) = (a^2b^2)/y^3`
If x= a cos θ, y = b sin θ, show that `a^2[y(d^2y)/(dx^2) + (dy/dx)^2] + b^2` = 0.
Find `"dy"/"dx"` if, yex + xey = 1
If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______
If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.
`"If" log(x+y) = log(xy)+a "then show that", dy/dx=(-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx = (−y^2)/x^2`
