Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x:
(log x)log x, x > 1
Advertisements
उत्तर
Let y = (log x)log x
Taking log on both sides, we get
log y = log x log (log x) ....(1)
Differentiating (1) both sides with respect to x, we get,
`1/y dy/dx = log x* 1/log x * 1/x + log (log x) * 1/x`
= `1/x * [1 + log (log x)]`
`dy/dx = (log x)^(log x) * 1/x * [1 + log (log x)]`, x > 1
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t. x:
`e^x/sinx`
Differentiate the following w.r.t. x:
`e^(sin^(-1) x)`
Differentiate the following w.r.t. x:
`e^(x^3)`
Differentiate the following w.r.t. x:
sin (tan–1 e–x)
Differentiate the following w.r.t. x:
`cos x/log x`, x > 0
Differentiate the following w.r.t. x:
cos (log x + ex), x > 0
Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.
If xy - yx = ab, find `(dy)/(dx)`.
If `"x" = "e"^(cos2"t") "and" "y" = "e"^(sin2"t")`, prove that `(d"y")/(d"x") = - ("y"log"x")/("x"log"y")`.
If xy = ex–y, prove that `("d"y)/("d"x) = logx/(1 + logx)^2`
If x = `e^(x/y)`, then prove that `dy/dx = (x - y)/(xlogx)`.
If y = `(cos x)^((cos x)^((cosx)....oo)`, show that `"dy"/"dx" = (y^2 tanx)/(y log cos x - 1)`
Find `"dy"/"dx"`, if y = `x^tanx + sqrt((x^2 + 1)/2)`
If `"y" = ("x" + sqrt(1 + "x"^2))^"n", "then" (1 + "x"^2) ("d"^2 "y")/"dx"^2 + "x" ("dy")/("dx")` is ____________.
If `"y = a"^"x", "b"^(2"x" -1), "then" ("d"^2"y")/"dx"^2` is ____________.
If `"y" = (varphi "n x")/"x",` then the value of y'' (e) is ____________.
If `"y"^2 = "ax"^2 + "bx + c", "then" "d"/"dx" ("y"^3 "y"_"z") =` ____________.
If `"xy"^2 = "ax"^2 + "bxy" + "y"^2, "then find" "dy"/"dx"`
If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then" "dy"/"dx"` is equal to ____________.
For positive values of \[x\], which expression grows faster than \[x^n\] for any fixed positive integer \[n\] when \[x\] is sufficiently large?
What is \[\frac{d}{dx}(e^x)\]?
Which expression gives the change of base rule?
Which expression gives the product rule for logarithms?
Which inverse property is valid only for \[x>0\]?
What is the domain of the exponential function \[y=b^x\]?
What is the domain of the logarithmic function \[y=\log_b x\]?
What is the range of the logarithmic function \[y=\log_b x\]?
Through which point does every graph of \[y=\log_b x\] pass?
If \[y=b^x\], which equivalent logarithmic statement is correct?
Which pair of graphs are reflections of each other about \[y=x\]?
Differentiate \[\cos^{-1}(e^x)\] with respect to \[x\].
Differentiate \[e^{\cos x}\] with respect to \[x\].
