Advertisements
Advertisements
प्रश्न
If y = x log x, then `(d^2y)/dx^2`= ______.
Advertisements
उत्तर
If y = x log x, then `(d^2y)/dx^2`= `bb(underline(1/x))`
Explanation:
y = x log x
Differentiating both sides,
`dy/dx = x * d/dx(logx) + logx * d/dx(x)`
= `x * 1/x + logx` = 1 + logx
Again differentiating w.r.t.x,
`d/dx(dy/dx) = d/dx(1) + d/dx(logx)`
`(d^2y)/(dx^2) = 0 + 1/x`
= `1/x`
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("x"^"2x")`
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`
Fill in the blank.
If y = y = [log (x)]2 then `("d"^2"y")/"dx"^2 =` _____.
State whether the following is True or False:
If y = log x, then `"dy"/"dx" = 1/"x"`
The derivative of ax is ax log a.
Solve the following:
If y = [log(log(logx))]2, find `"dy"/"dx"`
Find `"dy"/"dx"` if y = `"x"^"x" + ("7x" - 1)^"x"`
If u = 5x and v = log x, then `("du")/("dv")` is ______
State whether the following statement is True or False:
If y = log(log x), then `("d"y)/("d"x)` = logx
Find `(dy)/(dx)`, if xy = yx
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Find `("d"y)/("d"x)`, if y = xx + (7x – 1)x
Find `("d"y)/("d"x)`, if y = `root(3)(((3x - 1))/((2x + 3)(5 - x)^2)`
If y = x . log x then `dy/dx` = ______.
If y = (log x)2 the `dy/dx` = ______.
Find`dy/dx if, y = x^(e^x)`
Find `dy/dx , if y^x = e^(x+y)`
Find `dy/dx, "if" y=sqrt((2x+3)^5/((3x-1)^3(5x-2)))`
Find `dy/dx,"if" y=x^x+(logx)^x`
Find `dy/dx` if, y = `x^(e^x)`
Find `dy / dx` if, `y = x^(e^x)`
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/dx "if", y = x^(e^x)`
Find `dy/(dx)` if, `y = x^(e^x)`
Find `dy/(dx)` if, `x = e^(3t), y = e^sqrtt`.
