हिंदी

Find dy/dx in the following: 2x + 3y = sin x - Mathematics

Advertisements
Advertisements

प्रश्न

Find `bb(dy/dx)` in the following:

2x + 3y = sin x

योग
Advertisements

उत्तर

2x + 3y = sin x

Differentiating both sides with respect to x,

⇒ `2 d/dx (x) + 3 d/dx (y) = d/dx(sin x)`

⇒ `2 xx 1 + 3 dy/dx = cos x`

⇒ `3 dy/dx = cos x - 2`

`dy/dx = (cos x - 2)/3`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity and Differentiability - Exercise 5.3 [पृष्ठ १६९]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 5 Continuity and Differentiability
Exercise 5.3 | Q 1 | पृष्ठ १६९

संबंधित प्रश्न

Find `bb(dy/dx)` in the following:

sin2 y + cos xy = k


if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`


Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.


Find `"dy"/"dx"` ; if y = cos-1 `("2x" sqrt (1 - "x"^2))`


Differentiate e4x + 5 w.r..t.e3x


Find `"dy"/"dx"`, if : x = sinθ, y = tanθ


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 = 2 cos t + cos 2t, y = 2 sin t – sin 2t at t = `pi/(4)`


Differentiate `cos^-1((1 - x^2)/(1 + x^2)) w.r.t. tan^-1 x.`


Find `(d^2y)/(dx^2)` of the following : x = a cos θ, y = b sin θ at θ = `π/4`.


If x = a sin t – b cos t, y = a cos t + b sin t, show that `(d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)`.


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 : apx+q 


Find the nth derivative of the following : sin (ax + b)


Find the nth derivative of the following : `(1)/(3x - 5)`


Find the nth derivative of the following:

y = e8x . cos (6x + 7)


Choose the correct option from the given alternatives :

If f(x) = `sin^-1((4^(x + 1/2))/(1 + 2^(4x)))`, which of the following is not the derivative of f(x)?


Solve the following : 

f(x) = –x, for – 2 ≤ x < 0
= 2x, for 0 ≤ x < 2
= `(18 - x)/(4)`, for 2 < x ≤ 7
g(x) = 6 – 3x, for 0 ≤ x < 2
= `(2x - 4)/(3)`, for 2 < x ≤ 7
Let u (x) = f[g(x)], v(x) = g[f(x)] and w(x) = g[g(x)]. Find each derivative at x = 1, if it exists i.e. find u'(1), v' (1) and w'(1). If it doesn't exist, then explain why?


Differentiate the following w.r.t. x : `cos^-1((sqrt(1 + x) - sqrt(1 - x))/2)`


If x= a cos θ, y = b sin θ, show that `a^2[y(d^2y)/(dx^2) + (dy/dx)^2] + b^2` = 0.


If y = Aemx + Benx, show that y2 – (m + n)y1 + mny = 0.


Choose the correct alternative.

If y = 5x . x5, then `"dy"/"dx" = ?` 


State whether the following is True or False:

The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`


If x = a t4 y = 2a t2 then `("d"y)/("d"x)` = ______


If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______


State whether the following statement is True or False:

If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt("a"))`


`(dy)/(dx)` of `xy + y^2 = tan x + y` is


Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`


y = `e^(x3)`


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 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 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 log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×