Advertisements
Advertisements
प्रश्न
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
Advertisements
उत्तर
x = sin θ
Differentiating w. r. t. θ, we get
`("d"x)/("d"theta) = "d"/("d"theta) (sintheta)` = cos θ
y = tan θ
Differentiating w. r. t. θ, we get
`("d"y)/("d"theta) = "d"/("d"theta) (tantheta)` = sec2 θ
∴ `("d"y)/("d"x) = ((("d"y)/("d"theta)))/((("d"x)/("d"theta))`
= `(sec^2theta)/(cos theta)`
= sec3 θ
APPEARS IN
संबंधित प्रश्न
If y=eax ,show that `xdy/dx=ylogy`
If xpyq = (x + y)p+q then Prove that `dy/dx = y/x`
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
Find `bb(dy/dx)` in the following:
xy + y2 = tan x + y
Find `bb(dy/dx)` in the following:
sin2 x + cos2 y = 1
If for the function
\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]
Differentiate e4x + 5 w.r..t.e3x
Find `(dy)/(dx) if y = cos^-1 (√x)`
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
Discuss extreme values of the function f(x) = x.logx
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ
Find `"dy"/"dx"`, if : x = `(t + 1/t)^a, y = a^(t+1/t)`, where a > 0, a ≠ 1, t ≠ 0.
Find `"dy"/"dx"` if : x = t + 2sin (πt), y = 3t – cos (πt) at t = `(1)/(2)`
Differentiate `tan^-1((x)/(sqrt(1 - x^2))) w.r.t. sec^-1((1)/(2x^2 - 1))`.
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/(x)) w.r.t tan^-1((2xsqrt(1 - x^2))/(1 - 2x^2))`.
If x = at2 and y = 2at, then show that `xy(d^2y)/(dx^2) + a` = 0.
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
Find the nth derivative of the following : (ax + b)m
Find the nth derivative of the following:
`(1)/x`
Find the nth derivative of the following : eax+b
Find the nth derivative of the following : sin (ax + b)
Find the nth derivative of the following : y = eax . cos (bx + c)
Choose the correct option from the given alternatives :
If y = sec (tan –1x), then `"dy"/"dx"` at x = 1, is equal to
Choose the correct option from the given alternatives :
If y = sin (2sin–1 x), then dx = ........
Choose the correct option from the given alternatives :
If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........
Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1:
| x | f(x) | g(x) | f')x) | g'(x) |
| 0 | 1 | 5 | `(1)/(3)` | |
| 1 | 3 | – 4 | `-(1)/(3)` | `-(8)/(3)` |
(i) The derivative of f[g(x)] w.r.t. x at x = 0 is ......
(ii) The derivative of g[f(x)] w.r.t. x at x = 0 is ......
(iii) The value of `["d"/"dx"[x^(10) + f(x)]^(-2)]_(x = 1_` is ........
(iv) The derivative of f[(x + g(x))] w.r.t. x at x = 0 is ...
Differentiate the following w.r.t. x : `tan^-1((sqrt(x)(3 - x))/(1 - 3x))`
Differentiate log `[(sqrt(1 + x^2) + x)/(sqrt(1 + x^2 - x)]]` w.r.t. cos (log x).
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/x)` w.r.t. `cos^-1(sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))))`
Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`
Find `"dy"/"dx"` if, x3 + y3 + 4x3y = 0
Find `"dy"/"dx"` if, yex + xey = 1
Find `"dy"/"dx"` if, `"x"^"y" = "e"^("x - y")`
Solve the following:
If `"e"^"x" + "e"^"y" = "e"^((x + y))` then show that, `"dy"/"dx" = - "e"^"y - x"`.
Choose the correct alternative.
If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2` then `"dy"/"dx"` = ?
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If y = `e^(m tan^-1x)` then show that `(1 + x^2) (d^2y)/(dx^2) + (2x - m) (dy)/(dx)` = 0
Find `(dy)/(dx)` if x + sin(x + y) = y – cos(x – y)
Find `dy/dx if, x= e^(3t), y = e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx` if , x = `e^(3t), y = e^(sqrtt)`
If y = `(x + sqrt(x^2 - 1))^m`, show that `(x^2 - 1)(d^2y)/(dx^2) + xdy/dx` = m2y
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
If log(x + y) = log(xy) + a, then show that `dy/dx = (-y^2)/x^2`
