Advertisements
Advertisements
प्रश्न
`8^x/x^8`
Advertisements
उत्तर
Let y = `8^x/x^8`
Taking log on both sides, we get,
log y = `log 8^x/x^8`
⇒ log y = `log 8^x - log x^8`
⇒ log y = x log 8 – 8 log x
Differentiating both sides w.r.t. x
⇒ `1/y * "dy"/"dx" = log 8.1 - 8/x`
⇒ `"dy"/"dx" = y [log 8 - 8/x]`
Hence, `"dy"/"dx" = 8^x/x^8 [log 8 - 8/x]`
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
(x + 3)2 . (x + 4)3 . (x + 5)4
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Differentiate the function with respect to x.
`x^(xcosx) + (x^2 + 1)/(x^2 -1)`
Find `bb(dy/dx)` for the given function:
xy = `e^((x - y))`
Find the derivative of the function given by f(x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f′(1).
If u, v and w are functions of x, then show that `d/dx(u.v.w) = (du)/dx v.w + u. (dv)/dx.w + u.v. (dw)/dx` in two ways-first by repeated application of product rule, second by logarithmic differentiation.
If cos y = x cos (a + y), with cos a ≠ ± 1, prove that `dy/dx = cos^2(a+y)/(sin a)`.
If y = `e^(acos^(-1)x)`, −1 ≤ x ≤ 1, show that `(1- x^2) (d^2y)/(dx^2) -x dy/dx - a^2y = 0`.
Evaluate
`int 1/(16 - 9x^2) dx`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
Find `"dy"/"dx"` if y = xx + 5x
Solve the following differential equation: (3xy + y2) dx + (x2 + xy) dy = 0
If y = (log x)x + xlog x, find `"dy"/"dx".`
If `log_10((x^3 - y^3)/(x^3 + y^3))` = 2, show that `dy/dx = -(99x^2)/(101y^2)`.
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
Find the second order derivatives of the following : x3.logx
Find the second order derivatives of the following : log(logx)
If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
`"d"/"dx" [(cos x)^(log x)]` = ______.
If `("f"(x))/(log (sec x)) "dx"` = log(log sec x) + c, then f(x) = ______.
`log (x + sqrt(x^2 + "a"))`
If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.
If y `= "e"^(3"x" + 7), "then the value" |("dy")/("dx")|_("x" = 0)` is ____________.
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` is equal to ______.
Find `dy/dx`, if y = (sin x)tan x – xlog x.
Evaluate:
`int log x dx`
Find the derivative of `y = log x + 1/x` with respect to x.
If xy = yx, then find `dy/dx`
What is \[\frac{1}{y}\cdot\frac{dy}{dx}\] for \[y=\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\]?
For \[y=x^{\sin x}\], \[x>0\], what equation results after taking logarithm on both sides?
Which derivative correctly represents differentiating \[\ln y\] carefully?
What condition must be ensured for an expression inside logarithm?
