Advertisements
Advertisements
प्रश्न
Differentiate y = etanx w.r. to x
Advertisements
उत्तर
y = etanx
∴ `("d"y)/("d"x) = "d"/("d"x) ("e"^(tanx))`
= `"e"^(tanx) * "d"/("d"x)(tan x)`
= `"e"^(tan x) * sec^2x`
APPEARS IN
संबंधित प्रश्न
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: `(8)/(3root(3)((2x^2 - 7x - 5)^11`
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Differentiate the following w.r.t.x: `sqrt(tansqrt(x)`
Differentiate the following w.r.t.x: cos2[log(x2 + 7)]
Differentiate the following w.r.t.x: sec[tan (x4 + 4)]
Differentiate the following w.r.t.x: `log[sec (e^(x^2))]`
Differentiate the following w.r.t.x: log[tan3x.sin4x.(x2 + 7)7]
Differentiate the following w.r.t.x:
`log(sqrt((1 - cos3x)/(1 + cos3x)))`
Differentiate the following w.r.t.x: `log(sqrt((1 - sinx)/(1 + sinx)))`
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:
y = (25)log5(secx) − (16)log4(tanx)
Differentiate the following w.r.t. x : `tan^-1(sqrt(x))`
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 : `sin^-1(x^(3/2))`
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((cos7x)/(1 + sin7x))`
Differentiate the following w.r.t. x :
`cos^-1((1 - x^2)/(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 ((1 - 9^x))/((1 + 9^x)`
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x : `tan^-1((2sqrt(x))/(1 + 3x))`
Differentiate the following w.r.t. x :
`(x + 1)^2/((x + 2)^3(x + 3)^4`
Differentiate the following w.r.t. x : `(x^5.tan^3 4x)/(sin^2 3x)`
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`
Differentiate the following w.r.t. x :
etanx + (logx)tanx
Differentiate the following w.r.t. x : `[(tanx)^(tanx)]^(tanx) "at" x = pi/(4)`
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
Solve the following :
The values of f(x), g(x), f'(x) and g'(x) are given in the following table :
| x | f(x) | g(x) | f'(x) | fg'(x) |
| – 1 | 3 | 2 | – 3 | 4 |
| 2 | 2 | – 1 | – 5 | – 4 |
Match the following :
| A Group – Function | B Group – Derivative |
| (A)`"d"/"dx"[f(g(x))]"at" x = -1` | 1. – 16 |
| (B)`"d"/"dx"[g(f(x) - 1)]"at" x = -1` | 2. 20 |
| (C)`"d"/"dx"[f(f(x) - 3)]"at" x = 2` | 3. – 20 |
| (D)`"d"/"dx"[g(g(x))]"at"x = 2` | 5. 12 |
If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`
If y = `tan^-1[sqrt((1 + cos x)/(1 - cos x))]`, find `("d"y)/("d"x)`
Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x
If x = `sqrt("a"^(sin^-1 "t")), "y" = sqrt("a"^(cos^-1 "t")), "then" "dy"/"dx"` = ______
Derivative of (tanx)4 is ______
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 ______
If x = p sin θ, y = q cos θ, then `dy/dx` = ______
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
If y = log (sec x + tan x), find `dy/dx`.
