Advertisements
Advertisements
प्रश्न
If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`
पर्याय
`(2 - "x")/"x"`
`("x" - 2)/"x"`
`("e - x")/"ex"`
`("x - e")/"ex"`
Advertisements
उत्तर
`bb(("x" - 2)/"x")`
Explanation:
y = log `("e"^"x"/"x"^2)`
= log (ex) − log (x2)
= x log e − log x2
y = x − log x2 ...(∵ log e = 1)
Differentiating w.r.t. 'x', we get
`"dy"/"dx"= 1 - 1/("x"^2)."d"/"dx" ("x"^2)`
= `1 - (2"x")/("x"^2)`
= `1 - 2/"x"`
= `("x"- 2)/"x"`
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
Find `"dy"/"dx"`if, y = `"e"^("x"^"x")`
Find `"dy"/"dx"`if, y = (2x + 5)x
If y = elogx then `dy/dx` = ?
If y = x log x, then `(d^2y)/dx^2`= ______.
State whether the following is True or False:
The derivative of `log_ax`, where a is constant is `1/(x.loga)`.
The derivative of ax is ax log a.
Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`
Find `"dy"/"dx"` if y = `"x"^"x" + ("7x" - 1)^"x"`
If y = `"a"^((1 + log"x"))`, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If y = log(log x), then `("d"y)/("d"x)` = logx
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
Find `(dy)/(dx)`, if xy = yx
Find `("d"y)/("d"x)`, if y = (log x)x + (x)logx
Find `("d"y)/("d"x)`, if y = `root(3)(((3x - 1))/((2x + 3)(5 - x)^2)`
If y = x . log x then `dy/dx` = ______.
FInd `dy/dx` if,`x=e^(3t), y=e^sqrtt`
Find `dy/dx "if", y = x^(e^x)`
Find `dy/dx , if y^x = e^(x+y)`
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, `x = e^(3t), y = e^sqrtt`.
