Advertisements
Advertisements
Question
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Advertisements
Solution
Let y = `"cosec"^-1[1/cos(5^x)]`
= cosec–1[sec(5x)]
= `"cosec"^-1["cosec"(pi/2 - 5^x)]`
= `pi/(2) - 5^x`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(pi/2 - 5^x)`
= `"d"/"dx"(pi/2) - "d"/"dx"(5^x)`
= 0 –5x.log5
= –5x.log5.
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t.x:
`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
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: `e^(3sin^2x - 2cos^2x)`
Differentiate the following w.r.t.x: cos2[log(x2 + 7)]
Differentiate the following w.r.t.x: (1 + 4x)5 (3 + x −x2)8
Differentiate the following w.r.t.x:
`(x^3 - 5)^5/(x^3 + 3)^3`
Differentiate the following w.r.t.x:
`sqrt(cosx) + sqrt(cossqrt(x)`
Differentiate the following w.r.t.x:
log (sec 3x+ tan 3x)
Differentiate the following w.r.t.x:
`log(sqrt((1 + cos((5x)/2))/(1 - cos((5x)/2))))`
Differentiate the following w.r.t. x : cosec–1 (e–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 : `sin^-1(x^(3/2))`
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Differentiate the following w.r.t. x : `sin^4[sin^-1(sqrt(x))]`
Differentiate the following w.r.t.x:
tan–1 (cosec x + cot x)
Differentiate the following w.r.t. x : `sin^-1((4sinx + 5cosx)/sqrt(41))`
Differentiate the following w.r.t. x : `cos^-1((3cos3x - 4sin3x)/5)`
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 :
`sin^-1(4^(x + 1/2)/(1 + 2^(4x)))`
Differentiate the following w.r.t. x : `tan^-1((2sqrt(x))/(1 + 3x))`
Differentiate the following w.r.t. x : `root(3)((4x - 1)/((2x + 3)(5 - 2x)^2)`
Differentiate the following w.r.t. x : `(x^2 + 3)^(3/2).sin^3 2x.2^(x^2)`
Differentiate the following w.r.t. x : `((x^2 + 2x + 2)^(3/2))/((sqrt(x) + 3)^3(cosx)^x`
Differentiate the following w.r.t. x:
`x^(x^x) + e^(x^x)`
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Differentiate the following w.r.t. x :
(sin x)tanx + (cos x)cotx
Differentiate the following w.r.t. x : `10^(x^(x)) + x^(x(10)) + x^(10x)`
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 : `e^((x^7 - y^7)/(x^7 + y^7)` = a
Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x
If f(x) = 3x - 2 and g(x) = x2, then (fog)(x) = ________.
If x = `sqrt("a"^(sin^-1 "t")), "y" = sqrt("a"^(cos^-1 "t")), "then" "dy"/"dx"` = ______
If y = `1 + x + x^2/(2!) + x^3/(3!) + x^4/(4!) + .....,` then `(d^2y)/(dx^2)` = ______
If y = cosec x0, then `"dy"/"dx"` = ______.
If x = p sin θ, y = q cos θ, then `dy/dx` = ______
Find `(dy)/(dx)`, if x3 + x2y + xy2 + y3 = 81
The value of `d/(dx)[tan^-1((a - x)/(1 + ax))]` is ______.
Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.
If `cos((x^2 - y^2)/(x^2 + y^2))` = log a, show that `dy/dx = y/x`
