Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x.
(log x)cos x
Advertisements
उत्तर
Let, y = (log x)cos x
Taking logarithm of both sides,
log y = log (log x)cos x
= cos x log (log x) ...[∵ log mn = n log m]
Differentiating both sides with respect to x,
`1/y dy/dx = cos x d/dx log (log x) + log (log x) d/dx cos x`
`1/y dy/dx = cos x * 1/(log x) d/dx (log x) + log (log x) (- sin x)`
`1/y dy/dx = cos x * 1/(log x) * 1/x - sin x log (log x)`
`1/y dy/dx = - sin x log (log x) + (cos x)/(x log x)`
`dy/dx = y [- sin x log (log x) + (cos x)/(x log x)]`
`dy/dx = (log x)^(cos x) [- sin x log (log x) + (cos x)/(x log x)]`
APPEARS IN
संबंधित प्रश्न
If `y=log[x+sqrt(x^2+a^2)]` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`
Differentiate the function with respect to x.
xx − 2sin x
Differentiate the function with respect to x.
`(x + 1/x)^x + x^((1+1/x))`
Differentiate the function with respect to x.
(log x)x + xlog x
Find `bb(dy/dx)` for the given function:
yx = xy
Differentiate (x2 – 5x + 8) (x3 + 7x + 9) in three ways mentioned below:
- By using the product rule.
- By expanding the product to obtain a single polynomial.
- By logarithmic differentiation.
Do they all give the same answer?
If y = `e^(acos^(-1)x)`, −1 ≤ x ≤ 1, show that `(1- x^2) (d^2y)/(dx^2) -x dy/dx - a^2y = 0`.
if `x^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
Evaluate
`int 1/(16 - 9x^2) dx`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
Solve the following differential equation: (3xy + y2) dx + (x2 + xy) dy = 0
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
If y = `x^(x^(x^(.^(.^.∞))`, then show that `"dy"/"dx" = y^2/(x(1 - logy).`.
If x = esin3t, y = ecos3t, then show that `dy/dx = -(ylogx)/(xlogy)`.
If x = a cos3t, y = a sin3t, show that `"dy"/"dx" = -(y/x)^(1/3)`.
If x = log(1 + t2), y = t – tan–1t,show that `"dy"/"dx" = sqrt(e^x - 1)/(2)`.
If x = sin–1(et), y = `sqrt(1 - e^(2t)), "show that" sin x + dy/dx` = 0
Differentiate 3x w.r.t. logx3.
Find the second order derivatives of the following : log(logx)
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)`
Derivative of loge2 (logx) with respect to x is _______.
If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______
If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`
`2^(cos^(2_x)`
`log (x + sqrt(x^2 + "a"))`
If y `= "e"^(3"x" + 7), "then the value" |("dy")/("dx")|_("x" = 0)` is ____________.
If `f(x) = log [e^x ((3 - x)/(3 + x))^(1/3)]`, then `f^'(1)` is equal to
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.
The derivative of x2x w.r.t. x is ______.
Find `dy/dx`, if y = (sin x)tan x – xlog x.
The derivative of log x with respect to `1/x` is ______.
If \[y=x^x+x^{\frac{1}{x}}\] then \[\frac{\mathrm{d}y}{\mathrm{d}x}\] is equal to
