# How solve it? Topic: DERIVATE

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Please I need help I do not know how to solve

Please I need help I do not know how to solve

##### 2 Answers

#f(x)=sqrt(2x)#

First, let's rewrite the square root as a

#f(x)=(2x)^(1/2)#

Now, we need to recognize that these can be split up as a constant and a variable function.

#f(x)=2^(1/2)*x^(1/2)#

When we differentiate, multiplicative constants like the

To differentiate

Then, we see that:

#f'(x)=2^(1/2)*(1/2x^(1/2-1))#

Now simplifying:

#f'(x)=2^(1/2)/2x^(-1/2)#

#f'(x)=1/(2^(1/2)*x^(1/2))#

#f'(x)=1/sqrt(2x)#

So at

#f'(5/3)=1/sqrt(2*5/3)=1/sqrt(10/3)=sqrt(3/10)#

#### Explanation:

show below:

The derivative at