Advertisements
Advertisements
Question
Find `"dy"/"dx"` if cos (xy) = x + y
Advertisements
Solution
cos (xy) = x + y
Differentiating both sides w.r.t. x, we get
`-sin(xy)."d"/"dx"(xy) = 1 + "dy"/"dx"`
∴ `-sin(xy)[x"dy"/"dx" + y"d"/"dx"(x)] = 1 + "dy"/"dx"`
∴ `-sin(xy)[x"dy"/"dx" + y xx 1] = 1 + "dy"/"dx"`
∴ `-xsin(xy)"dy"/"dx" - ysin(xy) = 1 + "dy"/"dx"`
∴ `-"dy"/"dx" -sin(xy)"dy"/"dx" = 1 + ysin(xy)`
∴ `-[1 + x sin(xy)]"dy"/"dx" = 1 + ysin(xy)`
∴ `"dy"/"dx" = (-[1 + ysin (xy)])/(1 + x sin(xy)`.
APPEARS IN
RELATED QUESTIONS
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
Find `"dy"/"dx"` if xey + yex = 1
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 = log(10x4 + 5x3 - 3x2 + 2)
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
If y = 2x2 + 22 + a2, then `"dy"/"dx" = ?`
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
Find `"dy"/"dx"`, if y = `2^("x"^"x")`.
If y = sec (tan−1x), then `dy/dx` at x = 1 is ______.
If x = cos−1(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______
If y = `1/sqrt(3x^2 - 2x - 1)`, then `("d"y)/("d"x)` = ?
Choose the correct alternative:
If y = `x^(sqrt(x))`, then `("d"y)/("d"x)` = ?
If y = x2, then `("d"^2y)/("d"x^2)` is ______
If u = x2 + y2 and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = ______
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
If y = (sin x2)2, then `("d"y)/("d"x)` is equal to ______.
If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`
If f(x) = |cos x|, find f'`((3pi)/4)`
If y = log (cos ex), then `"dy"/"dx"` is:
Differentiate the function from over no 15 to 20 sin (x2 + 5)
y = cos (sin x)
y = sin (ax+ b)
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
If y = em sin–1 x and (1 – x2) = Ay2, then A is equal to ______.
If y = 2x2 + a2 + 22 then `dy/dx` = ______.
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^(5x^2 - 2x + 4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
lf y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, such that the composite function y = f[g(x)] is a differentiable function of x, then prove that:
`dy/dx = dy/(du) xx (du)/dx`
Hence, find `d/dx[log(x^5 + 4)]`.
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
If x = Φ(t) is a differentiable function of t, then prove that:
`int f(x)dx = int f[Φ(t)]*Φ^'(t)dt`
Hence, find `int(logx)^n/x dx`.
If y = `log((x + sqrt(x^2 + a^2))/(sqrt(x^2 + a^2) - x))`, find `dy/dx`.
Find `dy/dx` if, y = `e^(5x^2 -2x + 4)`
If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`
If `y=root5((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)`
If `y = (x + sqrt(a^2 + x^2))^m`, prove that `(a^2 + x^2)(d^2y)/(dx^2) + xdy/dx - m^2y = 0`
