Answer:
The derivative of function [tex]f(x)=5\sqrt{x}[/tex] is [tex]\frac{5}{2\sqrt{x} }[/tex]
Step-by-step explanation:
We need to find derivative of the given function [tex]f(x)=5\sqrt{x}[/tex]
Finding the derivative:
[tex]\frac{d}{dx}(5\sqrt{x} )[/tex]
Using the rule (a.f)' = a(f)', taking out constant value 5
[tex]=5\frac{d}{dx}(\sqrt{x} )[/tex]
We know [tex]\sqrt{x} =x^{\frac{1}{2}[/tex] Replacing [tex]\sqrt{x}[/tex]
[tex]=5\frac{d}{dx}(x^{\frac{1}{2}} )[/tex]
Applying derivative rule: [tex]\frac{d}{dx}(x^a)= a.x^{a-1}[/tex]
[tex]=5\times\frac{1}{2}(x^{\frac{1}{2}-1} )\\=\frac{5}{2}(x^{-\frac{1}{2}} )\\=\frac{5}{2x^{\frac{1}{2}}}\\=\frac{5}{2\sqrt{x} }[/tex]
So, the derivative of function [tex]f(x)=5\sqrt{x}[/tex] is [tex]\frac{5}{2\sqrt{x} }[/tex]
