Advertisements
Advertisements
प्रश्न
Fill in the blank.
If x = t log t and y = tt, then `"dy"/"dx"` = ____
Advertisements
उत्तर
If x = t log t and y = tt, then `"dy"/"dx"` = y.
Explanation:
x = t . log t ....(i)
y = tt
Taking logarithm of both sides, we get
log y = t . log t
∴ log y = x ....[From (i)]
∴ y = `"e"^"x"` ...(ii)
Differentiating both sides w.r.t. x, we get
`"dy"/"dx" = "e"^"x"`
∴ `"dy"/"dx" = "y"` ....[From (ii)]
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("x"^"2x")`
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
Find `"dy"/"dx"`if, y = `(1 + 1/"x")^"x"`
Find `"dy"/"dx"`if, y = `(log "x"^"x") + "x"^(log "x")`
Find `dy/dx`if, y = `(x)^x + (a^x)`.
Find `"dy"/"dx"`if, y = `10^("x"^"x") + 10^("x"^10) + 10^(10^"x")`
Fill in the blank.
If y = y = [log (x)]2 then `("d"^2"y")/"dx"^2 =` _____.
State whether the following is True or False:
The derivative of `log_ax`, where a is constant is `1/(x.loga)`.
State whether the following is True or False:
If y = log x, then `"dy"/"dx" = 1/"x"`
Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`
Differentiate log (1 + x2) with respect to ax.
If xy = 2x – y, then `("d"y)/("d"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
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
Find `("d"y)/("d"x)`, if x = `sqrt(1 + "u"^2)`, y = log(1 +u2)
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
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 = (log x)2 the `dy/dx` = ______.
Find `dy/dx` if, y = `x^(e^x)`
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))`
