Derivatives

[Crys0925]

I am trying to figure out the derivative of 5 times the square root of x. 5(sqrt of x)The square root is what is throwing me off. Any help?

 

[jwpaine]

I am trying to figure out the derivative of 5 times the square root of x. The square root is what is throwing me off. Any help?

derivative of \(\displaystyle \L5x^{2} = 2 \cdot 5x^{2-1} = 10x^{1} = 10x\)

 

[Deleted member 4993]

I am trying to figure out the derivative of 5 times the square root of x. 5(sqrt of x)The square root is what is throwing me off. Any help?

\(\displaystyle \frac{d}{dx}(x^n) = nx^{(n-1)}\)

in your case n = 1/2

so

\(\displaystyle \frac{d}{dx}(x^{\frac{1}{2}}) = \frac{1}{2}x^{(\frac{1}{2}-1)} = \frac{1}{2}x^{(-\frac{1}{2})} = \frac{1}{(2sqrt{x})}\)