Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x:
log (log x), x > 1
Advertisements
उत्तर
Let, y = log (log x)
Differentiating both sides with respect to x,
`dy/dx = d/dx log (log x)`
= `1/(log x) d/dx log x`
= `1/(log x) * 1/x`
= `1/(x log x)`, x > 1
APPEARS IN
संबंधित प्रश्न
Differentiate 3x w.r.t. log3x
Differentiate the following w.r.t. x:
`e^(sin^(-1) x)`
Differentiate the following w.r.t. x:
sin (tan–1 e–x)
Differentiate the following w.r.t. x:
log (cos ex)
Differentiate the following w.r.t. x:
`e^x + e^(x^2) + "..." + e^(x^5)`
Differentiate the following w.r.t. x:
`sqrt(e^(sqrtx))`, x > 0
Differentiate the following w.r.t. x:
cos (log x + ex), x > 0
Differentiate the function with respect to x:
(log x)log x, x > 1
Differentiate the function with respect to x:
cos (a cos x + b sin x), for some constant a and b.
Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.
The derivative of log10x w.r.t. x is ______.
If y = `(cos x)^((cos x)^((cosx)....oo)`, show that `"dy"/"dx" = (y^2 tanx)/(y log cos x - 1)`
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 `"x" = "a" ("cos" theta + theta "sin" theta), "y = a" ("sin" theta - theta "cos" theta), "then" ("d"^2 "y")/("dx"^2) =` ____________.
If `sqrt(("x + y")) + sqrt (("y - x")) = "a", "then" "dy"/"dx" =` ____________.
If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then" "dy"/"dx"` is equal to ____________.
If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.
The domain of the function defined by f(x) = logx 10 is
What is \[\frac{d}{dx}(e^x)\]?
Which expression gives the product rule for logarithms?
Which expression gives the quotient 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 \[y=\log_b x\]?
Through which point does every graph of \[y=\log_b x\] pass?
Which pair of graphs are reflections of each other about \[y=x\]?
For \[x>0\], differentiate \[\sin(\log x)\] with respect to \[x\].
Differentiate \[e^{\cos x}\] with respect to \[x\].
Which list contains the main log laws?
