Answer:
A: [tex]\frac{1}{2\sqrt{x-1} }[/tex]
B:[tex]\frac{1}{4\sqrt[4]{x^{3} } }[/tex]
c: 2x
Step-by-step explanation:
To find the derivative of x raised to the nth power we use the following template
[tex]x^{n}=nx^{n-1}[/tex]
Something else to keep in mind is that
[tex]\sqrt[n]{x^{y}}=x^{y/n}[/tex]
So knowing this we can rewrite a as follows
[tex]\sqrt{x-1} =(x-1)^{1/2}[/tex]
so we can use the template above and get
[tex]\frac{1}{2}(x-1)^{.5-1}[/tex]
So that simplifies to
[tex]\frac{1}{2}*(x-1)^{-\frac{1}{2}[/tex]
[tex]\frac{(x-1)^{-.5}}{2}[/tex]
[tex]\frac{1}{2\sqrt{x-1} }[/tex]
B: Same kind of deal here
[tex]\sqrt[4]{x}=x^{\frac{1}{4} }[/tex]
[tex]\frac{1}{4} *x^{\frac{1}{4}-1}[/tex]
[tex]\frac{x^{-\frac{3}{4}}}{4} =\frac{1}{4\sqrt[4]{x^{3} } }[/tex]
C: this one is by far the easiest because the derivative of a constant is 0 so we can just apply the same template from before and get
2x
