Question

Hi. I need help with these questions (see image)
Please show workings.
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Answer 1

A:
`(1)/(2√(x-1) )`

B:
`\frac{1}{4\sqrt[4]{x^(3) } }`

c: 2x

Explanation:

To find the derivative of x raised to the nth power we use the following template

`x^(n)=nx^(n-1)`

Something else to keep in mind is that

`\sqrt[n]{x^(y)}=x^(y/n)`

So knowing this we can rewrite a as follows

`√(x-1) =(x-1)^(1/2)`

so we can use the template above and get

`(1)/(2)(x-1)^(.5-1)`

So that simplifies to

`(1)/(2)*(x-1)^{-(1)/(2)`

`((x-1)^(-.5))/(2)`

`(1)/(2√(x-1) )`

B: Same kind of deal here

`\sqrt[4]{x}=x^{(1)/(4) }`

`(1)/(4) *x^{(1)/(4)-1}`

`\frac{x^{-(3)/(4)}}{4} =\frac{1}{4\sqrt[4]{x^(3) } }`

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