Question

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

Answer 1

Answer:

A: $\frac{1}{2\sqrt{x-1} }$

B:$\frac{1}{4\sqrt[4]{x^{3} } }$

c: 2x

Step-by-step 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

$\sqrt{x-1} =(x-1)^{1/2}$

so we can use the template above and get

$\frac{1}{2}(x-1)^{.5-1}$

So that simplifies to

$\frac{1}{2}*(x-1)^{-\frac{1}{2}$

$\frac{(x-1)^{-.5}}{2}$

$\frac{1}{2\sqrt{x-1} }$

B: Same kind of deal here

$\sqrt[4]{x}=x^{\frac{1}{4} }$

$\frac{1}{4} *x^{\frac{1}{4}-1}$

$\frac{x^{-\frac{3}{4}}}{4} =\frac{1}{4\sqrt[4]{x^{3} } }$

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