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

Differentiate the following:
y = `sqrt(1 + 2tanx)`

Differentiate the following:
y = sin³x + cos³x

Differentiate the following:
y = sin²(cos kx)

Differentiate the following:
y = (1 + cos²)⁶

Differentiate the following:

y = `"e"^(3x)/(1 + "e"^x`

Differentiate the following:
y = `sqrt(x +sqrt(x)`

Differentiate the following:
y = `"e"^(xcosx)`

Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`

Differentiate the following:
y = `sin(tan(sqrt(sinx)))`

Differentiate the following:

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

Find the derivatives of the following:
y = `x^(cosx)`

Find the derivatives of the following:
y = `x^(logx) + (logx)^x`

Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`

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)`