HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the derivative of the following function by the first principle: `x sqrtx`

Find the derivative of the following functions by the first principle: `1/(2x + 3)`

Differentiate the following function w.r.t.x. : `x/(x + 1)`

Differentiate the following function w.r.t.x : `(x^2 + 1)/x`

Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`

Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`

Differentiate the following function w.r.t.x. : `x/log x`

Differentiate the following function w.r.t.x. : `2^x/logx`

Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`

Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`

If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.

The demand function of a commodity is given as P = 20 + D − D². Find the rate at which price is changing when demand is 3.

Solve the following example: If the total cost function is given by; C = 5x³ + 2x² + 7; find the average cost and the marginal cost when x = 4.

Solve the following example: The total cost function of producing n notebooks is given by C= 1500 − 75n + 2n² + `"n"^3/5`. Find the marginal cost at n = 10.

Solve the following example: The total cost of ‘t’ toy cars is given by C=5(2^t)+17. Find the marginal cost and average cost at t = 3.

Solve the following example: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.

Solve the following example: The total cost of producing x units is given by C = 10e^2x, find its marginal cost and average cost when x = 2.

Solve the following example: The demand function is given as P = 175 + 9D + 25D² . Find the revenue, average revenue, and marginal revenue when demand is 10.

The supply S for a commodity at price P is given by S = P² + 9P − 2. Find the marginal supply when price is 7/-.

The cost of producing x articles is given by C = x² + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.