Advertisements
Advertisements
प्रश्न
If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`
उत्तर
Given `x^3y^5 = (x + y)^8`
Taking log on both sides
3 logx + 5 logy = 8 log(x + y)
Differentiate w.r.t. x
`3/x + 5/y (dy)/(dx) = 8(1/(x + y))[1 + (dy)/(dx)]`
`5/y (dy)/(dx) - 8/(x + y) dy/dx = 8/(x + y) - 3/x`
`(dy)/(dx)[5/y - 8/(x + y)] = (8x - 3x - 3y)/(x(x + y))`
`(dy)/(dx)[[5x + 5y - 8y]/(y(x + y))] = (5x - 3y)/(x(x + y))`
`(dy)/(dx) = [(5x - 3y)/(x(x + y)]] xx [(y(x + y))/(5x - 3y)]`
`(dy)/(dx) = y/x`
APPEARS IN
संबंधित प्रश्न
If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`
Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`
If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`
Find the second order derivative of the function.
x2 + 3x + 2
Find the second order derivative of the function.
`x^20`
Find the second order derivative of the function.
x . cos x
Find the second order derivative of the function.
log x
Find the second order derivative of the function.
x3 log x
Find the second order derivative of the function.
ex sin 5x
Find the second order derivative of the function.
tan–1 x
Find the second order derivative of the function.
log (log x)
If y = Aemx + Benx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`
If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2) = 49y`
If ey (x + 1) = 1, show that `(d^2y)/(dx^2) =((dy)/(dx))^2`
If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
Find `("d"^2"y")/"dx"^2`, if y = `sqrt"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"x"^5`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2
tan–1(x2 + y2) = a
If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1
If y = tan–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.
The derivative of cos–1(2x2 – 1) w.r.t. cos–1x is ______.
If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:
If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Find `(d^2y)/dx^2 if, y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Find `(d^2y)/(dx^2)` if, y = `e^((2x+1))`
Find `(d^2y)/dx^2` if, y = `e^((2x + 1))`
Find `(d^2y)/dx^2, "if" y = e^((2x+1))`
