Advertisements
Advertisements
Question
Differentiate the following w.r.t.x: sec[tan (x4 + 4)]
Advertisements
Solution
Let y = sec[tan (x4 + 4)]
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"{sec[tan(x^4 + 4)]}`
= `sec[tan(x^4 + 4)].tan[tan(x^4 + 4)]."d"/"dx"[tan(x^4 + 4)]`
= `sec[tan(x^4 + 4)].tan[tan(x^4 + 4)].sec^2(x^4 + 4)."d"/"dx"(x^4 + 4)`
= sec[tan(x4 + 4)]·tan[tan(x4 + 4)]·sec2(x4 + 4).(4x3 + 0)
= 4x3·sec2(x4 + 4)·sec[tan(x4 + 4)]·tan[tan(x4 + 4)].
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 + 4x - 7)`.
Differentiate the following w.r.t.x:
`sqrt(x^2 + sqrt(x^2 + 1)`
Differentiate the following w.r.t.x: cot3[log(x3)]
Differentiate the following w.r.t.x: cos2[log(x2 + 7)]
Differentiate the following w.r.t.x:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
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:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Differentiate the following w.r.t.x:
`log(sqrt((1 - cos3x)/(1 + cos3x)))`
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:
`log[a^(cosx)/((x^2 - 3)^3 logx)]`
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 : `tan^-1(sqrt(x))`
Differentiate the following w. r. t. x.
cos–1(1 – x2)
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 : `cos^-1(sqrt((1 + cosx)/2))`
Differentiate the following w.r.t. x :
`cos^-1(sqrt(1 - cos(x^2))/2)`
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 : `cot^-1((sin3x)/(1 + cos3x))`
Differentiate the following w.r.t. x : `tan^-1(sqrt((1 + cosx)/(1 - cosx)))`
Differentiate the following w.r.t. x : `sin^-1((4sinx + 5cosx)/sqrt(41))`
Differentiate the following w.r.t. x : `sin^-1((cossqrt(x) + sinsqrt(x))/sqrt(2))`
Differentiate the following w.r.t. x :
`cos^-1 ((1 - 9^x))/((1 + 9^x)`
Differentiate the following w.r.t. x : `sin^-1 ((1 - 25x^2)/(1 + 25x^2))`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x : `tan^-1((a + btanx)/(b - atanx))`
Differentiate the following w.r.t. x :
`tan^-1((5 -x)/(6x^2 - 5x - 3))`
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
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: `log((x^20 - y^20)/(x^20 + y^20))` = 20
Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sin((x^3 - y^3)/(x^3 + y^3))` = a3
Differentiate y = etanx w.r. to x
Differentiate sin2 (sin−1(x2)) w.r. to x
If f(x) = 3x - 2 and g(x) = x2, then (fog)(x) = ________.
If the function f(x) = `(log (1 + "ax") - log (1 - "bx))/x, x ≠ 0` is continuous at x = 0 then, f(0) = _____.
A particle moves so that x = 2 + 27t - t3. The direction of motion reverses after moving a distance of ______ units.
If x = p sin θ, y = q cos θ, then `dy/dx` = ______
Solve `x + y (dy)/(dx) = sec(x^2 + y^2)`
Differentiate `tan^-1 (sqrt((3 - x)/(3 + x)))` w.r.t. x.
Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.
