HSC Commerce (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

A manufacturing company produces x items at the total cost of Rs (180 + 4x). The demand function of this product is P = (240 − x). Find x for which profit is increasing.

Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.

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

Find `(dy)/(dx) if y = cos^-1 (√x)`

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

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)`.

If `sin^-1((x^5 - y^5)/(x^5 + y^5)) = pi/(6), "show that" "dy"/"dx" = x^4/(3y^4)`

If y = `sqrt(cosx + sqrt(cosx + sqrt(cosx + ... ∞)`, then show that `"dy"/"dx" = sinx/(1 - 2y)`.

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 = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`

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

Find `"dy"/"dx"`, if : x = a(1 – cosθ), y = b(θ – sinθ)