Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

sinⁿ (ax² + bx + c)

`cos(tan sqrt(x + 1))`

sinx² + sin²x + sin²(x²)

`sin^-1  1/sqrt(x + 1)`

(sin x)^cosx 

sin^mx . cosⁿx

(x + 1)²(x + 2)³(x + 3)⁴

`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`

`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`

`tan^-1 (secx + tanx), - pi/2 < x < pi/2`

`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`

`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`

`tan^-1 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`

`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`

If x^m . yⁿ = (x + y)^m+n, prove that `("d"^2"y")/("dx"^2)` = 0

If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.

For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.

Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`

Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.

Show that f(x) = 2x + cot^–1x + `log(sqrt(1 + x^2) - x)` is increasing in R