HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

Find `dy/dx if x^3 + y^2 + xy = 7`

Find `"dy"/"dx"` ; if x = sin³θ , y = cos³θ

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

Differentiate e^{4x + 5} w.r..t.e^3x

If x⁷ . y⁹ = (x + y)¹⁶ then show that `"dy"/"dx" = "y"/"x"`

Find `(dy)/(dx) , "If"   x^3 + y^2 + xy = 10`

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

If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`

Differentiate tan^-1 (cot 2x) w.r.t.x.

If x = tan^-1t and y = t³ , find `(dy)/(dx)`.

Discuss extreme values of the function f(x) = x.logx

If e^x + e^y = e^x+y, then show that `"dy"/"dx" = -e^(y - x)`.

Find `dy/dx`if, y = `(x)^x + (a^x)`.

Find `"dy"/"dx"`, if x = e^3t, y = `"e"^((4"t" + 5))`

If x = `(4t)/(1 + t^2),  y = 3((1 - t^2)/(1 + t^2))` then show that `dy/dx = (-9x)/(4y)`.

If x = t . log t, y = t^t, then show that `dy/dx - y = 0`.

If y = e^logx then `dy/dx` = ?

If y = 2x² + 2² + a², then `"dy"/"dx" = ?`

If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`