Find the derivative of

y=6x-6

from first principles.

Show, from first principles, that the derivative of

y=4x^2-3

is

8x.

Differentiate

f(x)=5x^3

from first principles.

Determine, from first principles, the derivative of

y=\left(1+x^2\right)^2

.

Find, from first principles, the derivative of

{y=\displaystyle\frac{1}{x}}

.

Find the derivative of

y=\sqrt{x}\,

from first principles.