HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find `dy/(dx)  "if", y = x^(e^(x))` 

Evaluate the following.

`intx^3 e^(x^2)dx`

Evaluate `int(1 + x + x^2/(2!))dx`.

Evaluate the following.

`intx^3/(sqrt(1 + x^4))dx`

Find `dy/(dx)` if, `y = x^(e^x)`

Find `dy/(dx)` if, `x = e^(3t),  y = e^sqrtt`.

Evaluate.

`int(5x^2 - 6x + 3)/(2x - 3)  dx`

Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.

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