HSC Arts कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find the derivatives of the following:

`tan^-1 = ((6x)/(1 - 9x^2))`

Find the derivatives of the following:

`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`

Find the derivatives of the following:

x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`

Find the derivatives of the following:

x = a (cos t + t sin t); y = a (sin t – t cos t)

Find the derivatives of the following:

x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`

Find the derivatives of the following:

`cos^-1 ((1 - x^2)/(1 + x^2))`

Find the derivatives of the following:

sin^-1 (3x – 4x³)

Find the derivatives of the following:

`tan^-1 ((cos x + sin x)/(cos x - sin x))`

Find the derivatives of the following:

Find the derivative of sin x² with respect to x² 

Find the derivatives of the following:

Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`

Find the derivatives of the following:

If u = `tan^-1  (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`

Find the derivatives of the following:

Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`

Find the derivatives of the following:

If y = sin^–1x then find y”

Find the derivatives of the following:

If y = e^tan–1x, show that (1 + x²)y” + (2x – 1)y’ = 0

Find the derivatives of the following:

If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x²)y₂ – 3xy₁ – y = 0

Find the derivatives of the following:

If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yⁿ = `1/"a"`

Find the derivatives of the following:

If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ

Find the derivatives of the following:

If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y₂ when x = 0

Choose the correct alternative:

`"d"/("d"x) (2/pi sin x^circ)` is

Choose the correct alternative:

If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is