HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Find the derivatives of the following:
x^y = y^x

Find the derivatives of the following:

(cos x)^{log x}

Find the derivatives of the following:

`x^2/"a"^2 + y^2/"b"^2` = 1

Find the derivatives of the following:

`sqrt(x^2 + y^2) = tan^-1 (y/x)`

Find the derivatives of the following:
tan (x + y) + tan (x – y) = x

Find the derivatives of the following:

If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`

Find the derivatives of the following:

`tan^-1sqrt((1 - cos x)/(1 + cos x)` 

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”