Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t.x: `log[(ex^2(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Advertisements
उत्तर
Let y = `log[(e^(x^2)(5 - 4x)^(3/2))/root(3)(7 - 6x)]`
Using
log(A.B) = logA + logB
y = `loge^(x^2) + log(((5 - 4x)^(3/2))/root(3)(7 - 6x))`
= `loge^(x^2) + log(5 - 4x)^(3/2) - log(root(3)(7 - 6x))`
= `x^2loge + 3/2log(5 - 4x) - log(7 - 6x)^(1/3)`
= `x^2 + 3/2log(5 - 4x) - 1/3log(7 - 6x)`
Now,
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"x^2 + 3/2"d"/"dx"log(5 - 4x) - 1/3"d"/"dx"log(7 - 6x)`
= `2x + (3)/(2)(1)/(5 - 4x)(-4) - (1)/(3)(1)/((7 - 6x))x(-6)`
= `2x - (6)/((5 - 4x)) + (2)/((7 - 6x)`
`2x - (6)/(5 - 4x) + (2)/(7 - 6x)`.
APPEARS IN
संबंधित प्रश्न
Differentiate the following w.r.t. x:
(x3 – 2x – 1)5
Differentiate the following w.r.t.x:
`(2x^(3/2) - 3x^(4/3) - 5)^(5/2)`
Differentiate the following w.r.t.x: `log[tan(x/2)]`
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Differentiate the following w.r.t.x: `e^(log[(logx)^2 - logx^2]`
Differentiate the following w.r.t.x: `sinsqrt(sinsqrt(x)`
Differentiate the following w.r.t.x: [log {log(logx)}]2
Differentiate the following w.r.t.x:
sin2x2 – cos2x2
Differentiate the following w.r.t.x:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
Differentiate the following w.r.t.x: `(1 + sinx°)/(1 - sinx°)`
Differentiate the following w.r.t.x: `cot(logx/2) - log(cotx/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 : tan–1(log x)
Differentiate the following w.r.t. x : cosec–1 (e–x)
Differentiate the following w.r.t. x : `tan^-1(sqrt(x))`
Differentiate the following w.r.t. x :
cos3[cos–1(x3)]
Differentiate the following w.r.t. x : `cot^-1[cot(e^(x^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(sqrt((1 + cosx)/(1 - cosx)))`
Differentiate the following w.r.t. x :
`cot^-1[(sqrt(1 + sin ((4x)/3)) + sqrt(1 - sin ((4x)/3)))/(sqrt(1 + sin ((4x)/3)) - sqrt(1 - sin ((4x)/3)))]`
Differentiate the following w.r.t. x : `"cosec"^-1[(10)/(6sin(2^x) - 8cos(2^x))]`
Differentiate the following w.r.t. x : `sin^-1((1 - x^2)/(1 + x^2))`
Differentiate the following w.r.t. x : cos–1(3x – 4x3)
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((8x)/(1 - 15x^2))`
Differentiate the following w.r.t. x : `cot^-1((4 - x - 2x^2)/(3x + 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^(tan^(-1)x`
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 : `sec((x^5 + y^5)/(x^5 - y^5))` = a2
Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x
Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x
Derivative of (tanx)4 is ______
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` = ______
If x = eθ, (sin θ – cos θ), y = eθ (sin θ + cos θ) then `dy/dx` at θ = `π/4` is ______.
Let f(x) be a polynomial function of the second degree. If f(1) = f(–1) and a1, a2, a3 are in AP, then f’(a1), f’(a2), f’(a3) are in ______.
If `cos((x^2 - y^2)/(x^2 + y^2))` = log a, show that `dy/dx = y/x`
Diffierentiate: `tan^-1((a + b cos x)/(b - a cos x))` w.r.t.x.
`lim_(x → 0) (sqrt(1 + x + x^2) − 1)/x` = ______.
