Advertisements
Advertisements
Question
Find `dy/dx`, if y = (log x)x.
Advertisements
Solution
y = (log x)x
Taking log of both sides,
log y = x log (logx)
Differentiating w.r.t. x,
`1/y dy/dx = x d/dx [log (log x)] + log (log x) d/dx (x)`
= `x * 1/(log x) * 1/x + log (log x) (1)`
`therefore dy/dx = y [1/(log x) + log (logx)]`
`therefore dy/dx = (log x)^x [1/(log x) + log (log x)]`
APPEARS IN
RELATED QUESTIONS
Differentiate the following function with respect to x: `(log x)^x+x^(logx)`
if xx+xy+yx=ab, then find `dy/dx`.
Differentiate the function with respect to x.
cos x . cos 2x . cos 3x
Differentiate the function with respect to x.
(log x)cos x
Differentiate the function with respect to x.
`(x + 1/x)^x + x^((1+1/x))`
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Differentiate the function with respect to x.
xsin x + (sin x)cos x
Find `bb(dy/dx)` for the given function:
xy + yx = 1
Find `bb(dy/dx)` for the given function:
(cos x)y = (cos y)x
Differentiate the function with respect to x:
xx + xa + ax + aa, for some fixed a > 0 and x > 0
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
Find `dy/dx` if y = xx + 5x
Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`
Solve the following differential equation: (3xy + y2) dx + (x2 + xy) dy = 0
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
If x = log(1 + t2), y = t – tan–1t,show that `"dy"/"dx" = sqrt(e^x - 1)/(2)`.
Find the second order derivatives of the following : x3.logx
Find the second order derivatives of the following : log(logx)
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
Find the nth derivative of the following: log (ax + b)
Choose the correct option from the given alternatives :
If xy = yx, then `"dy"/"dx"` = ..........
If f(x) = logx (log x) then f'(e) is ______
If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
lf y = `2^(x^(2^(x^(...∞))))`, then x(1 - y logx logy)`dy/dx` = ______
If xy = ex-y, then `"dy"/"dx"` at x = 1 is ______.
`8^x/x^8`
`log [log(logx^5)]`
If `"y" = "e"^(1/2log (1 + "tan"^2"x")), "then" "dy"/"dx"` is equal to ____________.
Given f(x) = `log((1 + x)/(1 - x))` and g(x) = `(3x + x^3)/(1 + 3x^2)`, then fog(x) equals
If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.
If y = `9^(log_3x)`, find `dy/dx`.
Find the derivative of `y = log x + 1/x` with respect to x.
If \[y=x^x+x^{\frac{1}{x}}\] then \[\frac{\mathrm{d}y}{\mathrm{d}x}\] is equal to
What is logarithmic differentiation?
If \[y=[u(x)]^{v(x)}\], which expression gives \[\frac{dy}{dx}\] in logarithmic differentiation?
What is \[\frac{1}{y}\cdot\frac{dy}{dx}\] for \[y=\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\]?
What is \[\frac{dy}{dx}\] for \[y=x^{\sin x}\], \[x>0\]?
Which derivative correctly represents differentiating \[\ln y\] carefully?
