Advertisements
Advertisements
Question
Differentiate the following w.r.t.x: `(e^sqrt(x) + 1)/(e^sqrt(x) - 1)`
Advertisements
Solution
Let y = `(e^sqrt(x) + 1)/(e^sqrt(x) - 1)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"((e^sqrt(x) + 1)/(e^sqrt(x) - 1))`
= `((e^sqrt(x) - 1)"d"/"dx"(e^sqrt(x) + 1) - (e^sqrt(x) + 1)"d"/"dx"(e^sqrt(x) - 1))/(e^sqrt(x) - 1)^2`
= `((e^sqrt(x) - 1)[e^sqrt(x)."d"/"dx"(sqrt(x)) + 0] - (e^sqrt(x) + 1)[e^sqrt(x)."d"/"dx"(sqrt(x)) - 0])/(e^sqrt(x) - 1)^2`
= `((e^sqrt(x) - 1)[e^sqrt(x) xx 1/(2sqrt(x))] - (e^sqrt(x) + 1)[e^sqrt(x) xx 1/(2sqrt(x))])/(e^sqrt(x) - 1)^2`
= `((e^sqrt(x))/(2sqrt(x))(e^sqrt(x) - 1 - e^sqrt(x) - 1))/(e^sqrt(x) - 1)^2`
= `(-e^sqrt(x))/(sqrt(x)(e^sqrt(x) - 1)^2`.
APPEARS IN
RELATED QUESTIONS
Differentiate the following w.r.t.x: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
Differentiate the following w.r.t.x: cot3[log(x3)]
Differentiate the following w.r.t.x: `5^(sin^3x + 3)`
Differentiate the following w.r.t.x: log[cos(x3 – 5)]
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: `x/(sqrt(7 - 3x)`
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: `(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[tan3x.sin4x.(x2 + 7)7]
Differentiate the following w.r.t.x: `log(sqrt((1 - sinx)/(1 + sinx)))`
Differentiate the following w.r.t.x:
y = (25)log5(secx) − (16)log4(tanx)
Differentiate the following w.r.t. x : tan–1(log x)
Differentiate the following w.r.t. x : cot–1(x3)
Differentiate the following w.r.t. x : `sin^4[sin^-1(sqrt(x))]`
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(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 :
`cos^-1[(3cos(e^x) + 2sin(e^x))/sqrt(13)]`
Differentiate the following w.r.t. x : `tan^-1((2x)/(1 - x^2))`
Differentiate the following w.r.t. x : `sin^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : `cos^-1((e^x - e^(-x))/(e^x + e^(-x)))`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Differentiate the following w.r.t. x : (logx)x – (cos x)cotx
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Differentiate the following w.r.t. x :
etanx + (logx)tanx
If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.
Differentiate y = `sqrt(x^2 + 5)` w.r. to x
If f(x) is odd and differentiable, then f′(x) is
If y = `tan^-1[sqrt((1 + cos x)/(1 - cos x))]`, find `("d"y)/("d"x)`
Differentiate sin2 (sin−1(x2)) w.r. to x
Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x
If the function f(x) = `(log (1 + "ax") - log (1 - "bx))/x, x ≠ 0` is continuous at x = 0 then, f(0) = _____.
If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) ______
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 ______
The weight W of a certain stock of fish is given by W = nw, where n is the size of stock and w is the average weight of a fish. If n and w change with time t as n = 2t2 + 3 and w = t2 - t + 2, then the rate of change of W with respect to t at t = 1 is ______
The differential equation of the family of curves y = `"ae"^(2(x + "b"))` is ______.
If y = cosec x0, then `"dy"/"dx"` = ______.
