Advertisements
Advertisements
प्रश्न
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
उत्तर
`y = sin^(-1) [(2.2^x)/(1 +(2^x)^2)]`
put 2x = tan θ
`∴ y = sin^(-1) [(2 tan theta ) /(1 + tan^2 theta)]`
= sin-1 [ sin 2θ ]
= 2θ
y = 2 tan-1 ( 2x )
Differentiating wrt x,
`(dy)/(dx) = 2/(1 +(2^x) )xx d/(dx) (2^x)`
`= 2/(1 + (2^x)^2) xx 2^x log 2 = (2 ^ (x+ 1))/(1 + 4^x) log 2 =" sin y log" 2`
APPEARS IN
संबंधित प्रश्न
Differentiate the following function with respect to x: `(log x)^x+x^(logx)`
if xx+xy+yx=ab, then find `dy/dx`.
Differentiate the function with respect to x.
cos x . cos 2x . cos 3x
Differentiate the function with respect to x.
(x + 3)2 . (x + 4)3 . (x + 5)4
Differentiate the function with respect to x.
`(sin x)^x + sin^(-1) sqrtx`
Find `dy/dx` for the function given in the question:
(cos x)y = (cos y)x
Find `dy/dx` for the function given in the question:
`xy = e^((x – y))`
Differentiate (x2 – 5x + 8) (x3 + 7x + 9) in three ways mentioned below:
- by using product rule
- by expanding the product to obtain a single polynomial.
- by logarithmic differentiation.
Do they all give the same answer?
If cos y = x cos (a + y), with cos a ≠ ± 1, prove that `dy/dx = cos^2(a+y)/(sin a)`
If ey ( x +1) = 1, then show that `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
xy = ex-y, then show that `"dy"/"dx" = ("log x")/("1 + log x")^2`
If y = `x^(x^(x^(.^(.^.∞))`, then show that `"dy"/"dx" = y^2/(x(1 - logy).`.
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
If x = 2cos4(t + 3), y = 3sin4(t + 3), show that `"dy"/"dx" = -sqrt((3y)/(2x)`.
If y = `log(x + sqrt(x^2 + a^2))^m`, show that `(x^2 + a^2)(d^2y)/(dx^2) + x "d"/"dx"` = 0.
If y = `log[sqrt((1 - cos((3x)/2))/(1 +cos((3x)/2)))]`, find `("d"y)/("d"x)`
`d/dx(x^{sinx})` = ______
`"d"/"dx" [(cos x)^(log x)]` = ______.
If y = `("e"^"2x" sin x)/(x cos x), "then" "dy"/"dx" = ?`
`2^(cos^(2_x)`
If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.
`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` is equal to ______.
If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`
If y = `9^(log_3x)`, find `dy/dx`.
Find `dy/dx`, if y = (log x)x.
If xy = yx, then find `dy/dx`
