Question

Using first principle, find the derivative of y = ^-1

Answer 1

Step-by-step explanation:

Let f(x)=

x

2

1

Thus according to first principle,

f

′

(x)=

h→0

lim

h

f(x+h)−f(x)

=

h→0

lim

h

(x+h)

1

−

x

2

1

=

h→0

lim

h

1

[

x

2

(x+h)

2

x−(x+h)

2

]

=

h→0

lim

h

1

[

x

2

(x+h)

2

x

2

−x

2

−h

2

−2hx

]

=

h→0

lim

h

1

[

x

2

(x+h)

2

−h

2

−2hx

]

=

h→0

lim

[

x

2

(x+h)

2

−h−2x

]

=

x

2

(x+0)

2

0−2x

=

x

3

−2

Answer 2

Answer:

Here is my derivation

= -1/x2