HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Important Questions for Mathematics and Statistics

If `y=cos^-1(2xsqrt(1-x^2))`, find dy/dx

If y=e^ax ,show that  `xdy/dx=ylogy`

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

find dy/dx if `y=tan^-1((6x)/(1-5x^2))`

If `y=sec^-1((sqrtx-1)/(x+sqrtx))+sin_1((x+sqrtx)/(sqrtx-1)), `

(A) x

(B) 1/x

(C) 1

(D) 0

If x^py^q = (x + y)^p+q then Prove that `dy/dx = y/x`

Find dy/dx if x sin y + y sin x = 0.

If y = f (x) is a differentiable function of x such that inverse function x = f ^–1(y) exists, then
prove that x is a differentiable function of y and 

`dx/dy=1/(dy/dx)`, Where `dy/dxne0`

Hence if `y=sin^-1x, -1<=x<=1 , -pi/2<=y<=pi/2`

then show that `dy/dx=1/sqrt(1-x^2)`, where  `|x|<1`

Find `dy/dx` if `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`

Differentiate tan^-1 (cot 2x) w.r.t.x.

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?  

Differentiate the following w.r.t.x:

tan[cos(sinx)]

Differentiate the following w.r.t. x: `x^(tan^(-1)x`

Differentiate the following w.r.t. x: x^e + x^x + e^x + e^e.

If `log_10((x^3 - y^3)/(x^3 + y^3))` = 2, show that `dy/dx = -(99x^2)/(101y^2)`.

If e^x + e^y = e^{(x + y)}, then show that `dy/dx = -e^(y - x)`.

If y = `log(x + sqrt(x^2 + a^2))^m`, show that `(x^2 + a^2)(d^2y)/(dx^2) + x "d"/"dx"` = 0.

If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.

If f(x) = log_x (log x) then f'(e) is ______

If y = `"e"^(1 + logx)` then find `("d"y)/("d"x)`