How solve it? Topic: DERIVATE
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