Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"` if, y = log(log x)
उत्तर
y = log(log x)
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"` [log (log x)]
`= 1/(log "x") * "d"/"dx" (log "x")`
`= 1/(log "x") * 1/"x"`
∴ `"dy"/"dx" = 1/("x" * log "x")`
APPEARS IN
संबंधित प्रश्न
If y = eax. cos bx, then prove that
`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
Find the second order derivatives of the following : xx
Find `"dy"/"dx"` if, y = `root(3)("a"^2 + "x"^2)`
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
Solve the following:
If y = (6x3 - 3x2 - 9x)10, find `"dy"/"dx"`
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`.
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)` = ______
State whether the following statement is True or False:
If y = ex, then `("d"^2y)/("d"x^2)` = ex
If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`
If f(x) = |cos x|, find f'`((3pi)/4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
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)]`.
If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = ______.
If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
Solve the following:
If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`
Find `(dy) / (dx)` if, `y = e ^ (5x^2 - 2x + 4)`