Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`
उत्तर
Let y = `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`
Then log y = `log[(4x - 1)/((2x + 3)(5 - 2x)^2)]^(1/3)`
= `(1)/(3)log[(4x - 1)/((2x + 3)(5 - 2x)^2)]`
= `(1)/(3)[log(4x - 1) - log(2x + 3)(5 - 2x)^2]`
= `(1)/(3)log(4x - 1) - (1)/(3)log(2x + 3) - (2)/(3)log(5 - 2x)`
Differentiating both sides w.r.t. x, we get
`(1)/y."dy"/"dx" = (1)/(3)"d"/"dx"[log(4x - 1)] - (1)/(3)"d"/"dx"[log(2x + 3)] - (2)/(3)"d"/"dx"[log(5 - 2x)]`
= `(1)/(3) xx (1)/(4x - 1)."d"/"dx"(4x - 1) - (1)/(3) xx (1)/(2x + 3)."d"/"dx"(2x + 3) - (2)/(3) xx (1)/(5 - 2x)."d"/"dx"(5 - 2x)`
= `(1)/(3(4x - 1)). (4 xx 1 - 0) - (1)/(3(2x + 3)).(2 xx 1 + 0) - (2)/(3(5 - 2x)).(0 - 2 xx 1)`
∴ `"dy"/"dx" = y[(4)/(3(4x - 1)) - (2)/(3(2x + 3)) + (4)/(3(5 - 2x))]`
= `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2))[(4)/(3(4x - 1)) - (2)/(3(2x + 3)) + (4)/(3(5 - 2x))]`.
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
Differentiate the following w.r.t.x:
`sqrt(e^((3x + 2) + 5)`
Differentiate the following w.r.t.x:
sin2x2 – cos2x2
Differentiate the following w.r.t.x: `x/(sqrt(7 - 3x)`
Differentiate the following w.r.t.x: (1 + sin2 x)2 (1 + cos2 x)3
Differentiate the following w.r.t.x: `(1 + sinx°)/(1 - sinx°)`
Differentiate the following w.r.t.x: `cot(logx/2) - log(cotx/2)`
Differentiate the following w.r.t.x: `log[4^(2x)((x^2 + 5)/(sqrt(2x^3 - 4)))^(3/2)]`
Differentiate the following w.r.t.x:
`(x^2 + 2)^4/(sqrt(x^2 + 5)`
Differentiate the following w.r.t. x : cosec–1 (e–x)
Differentiate the following w.r.t. x : cot–1(x3)
Differentiate the following w.r.t. x : cot–1(4x)
Differentiate the following w.r.t. x : `sin^-1(x^(3/2))`
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^2))]`
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Differentiate the following w.r.t. x : `tan^-1[(1 - tan(x/2))/(1 + tan(x/2))]`
Differentiate the following w.r.t. x : `"cosec"^-1((1)/(4cos^3 2x - 3cos2x))`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x : `sin^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x :
`sin^(−1) ((1 − x^3)/(1 + x^3))`
Differentiate the following w.r.t. x:
`tan^-1((2x^(5/2))/(1 - x^5))`
Differentiate the following w.r.t. x :
`tan^(−1)[(2^(x + 2))/(1 − 3(4^x))]`
Differentiate the following w.r.t. x :
`tan^-1((5 -x)/(6x^2 - 5x - 3))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 2))`
Differentiate the following w.r.t. x : `(x^5.tan^3 4x)/(sin^2 3x)`
Differentiate the following w.r.t. x : (sin x)x
Differentiate the following w.r.t. x : (sin xx)
Differentiate the following w.r.t. x :
etanx + (logx)tanx
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : x7.y5 = (x + y)12
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sec((x^5 + y^5)/(x^5 - y^5))` = a2
If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.
Differentiate sin2 (sin−1(x2)) w.r. to x
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
If y = `sin^-1[("a"cosx - "b"sinx)/sqrt("a"^2 + "b"^2)]`, then find `("d"y)/("d"x)`
y = {x(x - 3)}2 increases for all values of x lying in the interval.
If y = `(3x^2 - 4x + 7.5)^4, "then" dy/dx` is ______
