Question #48bee

2 Answers
Ryoksos
Mar 22, 2017

1/(2x)

Explanation:

To take the derivative of any natural log we take the argument and raise it to the negative first, in this case 1/(sqrt(x)). However because the argument is not just x we must apply the chain rule to it and multiply the expression we just found by the derivative of the argument alone.

The derivative of the argument sqrt(x) can be found using the chain rule and it is 1/(2*sqrt(x)). Now we multiply both expression together to get: 1/(2*sqrt(x)*sqrt(x)).

Multiplying two square roots with the same argument however just equals the argument so we can simplify this to the final solution 1/(2x). Hope this helped!

Steve M
Mar 22, 2017

dy/dx = 1/(2x)

Explanation:

We have:

y = lnsqrt(x)

Which we can write as:

y = lnx^(1/2)
\ \ = 1/2lnx (using the rule of logs)

Differentiating wrt x and using d/dxlnx=1/x; then:

dy/dx = 1/2 1/x = 1/(2x)

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