HSC Commerce: Marketing and Salesmanship 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

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)`.

If `x^y = e^(x - y)` , show that `(dy)/(dx) = logx/(1 + logx)^2`

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

The total cost function of a firm is C = x² + 75x + 1600 for output x. Find the  output for which the average cost ls minimum. Is C_A= C_m at this output?  

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

If x = 2at² , y = 4at, then `dy/dx = ?`

If x = `y + 1/y`, then `dy/dx` = ____.

If y = `e^(ax)`, then `x * dy/dx` = ______.

State whether the following is True or False:

The derivative of `log_ax`, where a is constant is `1/(x.loga)`.

The derivative of a^x is a^x log a.

If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`