Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x :
etanx + (logx)tanx
उत्तर
Let y = etanx + (logx)tanx
Put u = (logx)tanx
∴ log u = log (log x)tanx = (tan x).(log log x)
Differentiating both sides w.r.t. x, we get
`1/u."du"/"dx" = "d"/"dx"[(tan x).(log logx)]`
= `(tanx)."d"/"dx"(log log x) + (log log x)."d"/"dx"(tan x)`
= `tanx xx 1/logx."d"/"dx"(logx) + (log log x)(sec^2x)`
= `tanx xx 1/logx xx 1/x + (log log x)(sec^2x)`
∴ `"du"/"dx" = u[tanx/(xlogx) + (loglogx)(sec^2x)]`
= `(logx)^(tanx)[tanx(xlogx) + (log log x)(sec^2x)]`
Now, y = etanx + u
∴ `"dy"/"dx" = "d"/"dx"(e^tanx) + "du"/"dx"`
= `e^(tanx)."d"/"dx"(tanx) + "du"/"dx"`
= `e^(tanx).sec^2x + (logx)^(tanx)[tanx/(xlogx) + (log log x)(sec^2x)]`
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t.x:
`sqrt(x^2 + sqrt(x^2 + 1)`
Differentiate the following w.r.t.x:
`sqrt(e^((3x + 2) + 5)`
Differentiate the following w.r.t.x: `sqrt(tansqrt(x)`
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x: `log_(e^2) (log x)`
Differentiate the following w.r.t.x: (1 + 4x)5 (3 + x −x2)8
Differentiate the following w.r.t.x: (1 + sin2 x)2 (1 + cos2 x)3
Differentiate the following w.r.t.x:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Differentiate the following w.r.t.x: log[tan3x.sin4x.(x2 + 7)7]
Differentiate the following w.r.t.x:
`log(sqrt((1 + cos((5x)/2))/(1 - cos((5x)/2))))`
Differentiate the following w.r.t.x: `log[(ex^2(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Differentiate the following w.r.t.x:
`(x^2 + 2)^4/(sqrt(x^2 + 5)`
Differentiate the following w.r.t. x : tan–1(log x)
Differentiate the following w.r.t. x : cot–1(4x)
Differentiate the following w.r.t. x :
`sin^-1(sqrt((1 + x^2)/2))`
Differentiate the following w.r.t. x : cos–1(1 –x2)
Differentiate the following w.r.t. x : `cos^-1(sqrt((1 + cosx)/2))`
Differentiate the following w.r.t. x : `tan^-1(sqrt((1 + cosx)/(1 - cosx)))`
Differentiate the following w.r.t. x : `sin^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `sin^-1(2xsqrt(1 - x^2))`
Differentiate the following w.r.t. x : cos–1(3x – 4x3)
Differentiate the following w.r.t. x : `cos^-1((e^x - e^(-x))/(e^x + e^(-x)))`
Differentiate the following w.r.t. x :
`sin^-1(4^(x + 1/2)/(1 + 2^(4x)))`
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:
`cot^-1((1 + 35x^2)/(2x))`
Differentiate the following w.r.t. x :
`tan^-1((5 -x)/(6x^2 - 5x - 3))`
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `tan^-1((3x^2 - 4y^2)/(3x^2 + 4y^2))` = a2
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `e^((x^7 - y^7)/(x^7 + y^7)` = a
If y = sin−1 (2x), find `("d"y)/(""d"x)`
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x
Derivative of (tanx)4 is ______
The value of `d/(dx)[tan^-1((a - x)/(1 + ax))]` is ______.
