Advertisements
Advertisements
प्रश्न
If y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`, find `("d"y)/("d"x)`
Advertisements
उत्तर
y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`
= `log4^(2x) + log((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)`
= `2x log4 + 3/2[log(x^2 + 5)/(sqrt(2x^3 - 4))]`
= `2x log4 + 3/2[log(x^2 + 5) - logsqrt(2^3 - 4)]`
= `2x log4 + 3/2[log(x^2 + 5) - 3/4log(2x^3 - 4)]`
Differentiating w. r. t. x, we get
`("d"y)/("d"x) = "d"/("dx)[2xlog 4 + 3/2 log(x^2 + 5) - 3/4log(2x^3 - 4)]`
= `2log4*"d"/("d"x)(x) + 3/2*"d"/("d"x) [log(x^2 + 5)] - 3/4*"d"/("d"x) [log(2x^3 - 4)]`
= `2log4*1 + 3/*1/(x^2 + 5)*"d"/("d"x) (x^2 + 5) - 3/4*1/(2x^3 - 4)*"d"/("d"x)(2x^3 - 4)`
= `2log4 + 3/2*1/(x^2 + 5)*2x - 3/4*1/(2x^3 - 4)*6x^2`
∴ `("d"y)/("d"x) = 2log4 + (3x)/(x^2 + 5) - (9x^2)/(2(2x^3 - 4)`
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`
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.
`(x cos x)^x + (x sin x)^(1/x)`
Find `bb(dy/dx)` for the given function:
xy + yx = 1
Find `bb(dy/dx)` for the given function:
xy = `e^((x - y))`
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 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 x = a (cos t + t sin t) and y = a (sin t – t cos t), find `(d^2y)/dx^2`.
Find `dy/dx` if y = xx + 5x
Find `(d^2y)/(dx^2)` , if y = log x
Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`
If `"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)` , the show that `"dy"/"dx" = "y"/"x"`
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)`.
Differentiate 3x w.r.t. logx3.
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)`
Derivative of loge2 (logx) with respect to x is _______.
lf y = `2^(x^(2^(x^(...∞))))`, then x(1 - y logx logy)`dy/dx` = ______
If y = `{f(x)}^{phi(x)}`, then `dy/dx` is ______
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) = ______.
Derivative of `log_6`x with respect 6x to is ______
`2^(cos^(2_x)`
`8^x/x^8`
`log (x + sqrt(x^2 + "a"))`
`log [log(logx^5)]`
If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`
`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.
If `"f" ("x") = sqrt (1 + "cos"^2 ("x"^2)), "then the value of f'" (sqrtpi/2)` is ____________.
If `f(x) = log [e^x ((3 - x)/(3 + x))^(1/3)]`, then `f^'(1)` is equal to
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` is equal to ______.
The derivative of x2x w.r.t. x is ______.
Find `dy/dx`, if y = (sin x)tan x – xlog x.
If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`
The derivative of log x with respect to `1/x` is ______.
