Question

f'(x)/rootf(x) formula​

Answer 1

Answer:

The derivative of

√

x

is

1

2

√

x

.

Remember that we can rewrite surds like this in index notation. For this case,

√

x

=

x

1

2

.

Now we can simply use the power rule for differentiation, namely that

d

d

x

x

n

=

n

x

n

−

1

. Let

n

=

1

2

. Therefore:

d

d

x

x

1

2

=

1

2

x

1

2

−

1

=

1

2

x

−

1

2

=

1

2

×

1

√

x

=

1

2

√

x