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

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" = ?` 

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 f(x) = a^x, where a is constant is x.a^x-1.

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

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`

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

If y = sec (tan⁻¹x), then `dy/dx` at x = 1 is ______.

Find `("d"y)/("d"x)`, if y = [log(log(logx))]² 

Find `(dy)/(dx)`, if x^y = y^x 

Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`

Find `("d"y)/("d"x)`, if y = `root(3)(((3x - 1))/((2x + 3)(5 - x)^2)`

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