Question

Find the derivative of √e^√x​

Answer 1

Step-by-step explanation:

In this problem we have to use the chain rule.

y

=

e

√

x

=

e

x

1

2

, convert the square root to its rational power

Apply the chain rule and begin to simplify

y

'

=

e

√

x

⋅

(

1

2

)

x

1

2

−

1

y

'

=

e

√

x

⋅

(

1

2

)

x

1

2

−

2

2

y

'

=

e

√

x

⋅

(

1

2

)

x

−

1

2

y

'

=

(

e

√

x

2

)

x

−

1

2

Convert the exponents to positive numbers

y

'

=

e

√

x

2

x

1

2

y

'

=

e

√

x

2

√

x

Rationalize

y

'

=

e

√

x

2

√

x

⋅

(

√

x

√

x

)

y

'

=

e

√

x

√

x

2

x