HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

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

Differentiate the following w.r.t.x:

tan[cos(sinx)]

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following:

y = `sqrt(x)`

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)` 

If y = log [cos(x⁵)] then find `("d"y)/("d"x)`

Differentiate sin² (sin⁻¹(x²)) w.r. to x

Differentiate `cot^-1((cos x)/(1 + sinx))` w.r. to x

Differentiate `sin^-1((2cosx + 3sinx)/sqrt(13))` w.r. to x

If log₅ `((x^4 + "y"^4)/(x^4 - "y"^4))` = 2, show that `("dy")/("d"x) = (12x^3)/(13"y"^2)`

If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`

If x sin(a + y) + sin a cos(a + y) = 0 then show that `("d"y)/("d"x) = (sin^2("a" + y))/(sin"a")`

If `int (dx)/(4x^2 - 1)` = A log `((2x - 1)/(2x + 1))` + c, then A = ______.

If y = `e^(m tan^-1x)` then show that `(1 + x^2) (d^2y)/(dx^2) + (2x - m) (dy)/(dx)` = 0