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

Find the second order derivative of the function.

e^x sin 5x

Find the second order derivative of the function.

e^6x cos 3x

Find the second order derivative of the function.

tan^–1 x

Find the second order derivative of the function.

log (log x)

Find the second order derivative of the function.

sin (log x)

If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.

If y = cos^–1 x, find `(d^2y)/dx^2` in terms of y alone.

If y = 3 cos (log x) + 4 sin (log x), show that x²y₂ + xy₁ + y = 0.

If y = Ae^mx + Be^nx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`.

If y = 500e^7x + 600e^–7x, show that `(d^2y)/(dx^2)` = 49y.

If e^y (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.

If y = (tan^–1 x)², show that (x² + 1)² y₂ + 2x (x² + 1) y₁ = 2

Evaluate the definite integral:

`int_(-1)^1 (x + 1)dx`

Evaluate the definite integral:

`int_2^3 1/x dx`

Evaluate the definite integral:

`int_1^2 (4x^3 - 5x^2 + 6x + 9)  dx`

Evaluate the definite integral:

`int_0^(pi/4) sin2xdx`

Evaluate the definite integral:

`int_0^(pi/2) cos 2x  dx`

Evaluate the definite integral:

`int_4^5 e^x dx`

Evaluate the definite integral:

`int_0^(pi/4) tan x dx`

Evaluate the definite integral:

`int_(pi/6)^(pi/4) cosec x  dx`