HSC Commerce इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Differentiate the following with respect to x.

(ax² + bx + c)ⁿ

Differentiate the following with respect to x.

sin(x²)

Differentiate the following with respect to x.

`1/sqrt(1 + x^2)`

Find `"dy"/"dx"` for the following function

xy – tan(xy)

Find `"dy"/"dx"` for the following function.

x² – xy + y² = 1

Find `"dy"/"dx"` for the following function.

x³ + y³ + 3axy = 1

If `xsqrt(1 + y) + ysqrt(1 + x)` = 0 and x ≠ y, then prove that `"dy"/"dx" = - 1/(x + 1)^2`

If 4x + 3y = log(4x – 3y), then find `"dy"/"dx"`

Differentiate the following with respect to x.

x^{sin x}

Differentiate the following with respect to x.

(sin x)^x

Differentiate the following with respect to x.

(sin x)^{tan x}

Differentiate the following with respect to x.

`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`

If x^m . yⁿ = (x + y)^m+n, then show that `"dy"/"dx" = y/x`

Find `"dy"/"dx"` of the following function:

x = ct, y = `c/t`

Find `"dy"/"dx"` of the following function:

x = log t, y = sin t

Find `"dy"/"dx"` of the following function:

x = a cos³θ, y = a sin³θ

Find `"dy"/"dx"` of the following function:

x = a(θ – sin θ), y = a(1 – cos θ)

Differentiate sin³x with respect to cos³x.

Differentiate sin²x with respect to x².

Find y₂ for the following function:

y = e^3x+2