Help me to find function derivatives

Question

f(x)=3x-2√x;

f(x)=arcsin x-1/x+√2x-1;

f(x)=√1+ln²x?

Answer 1

(1).

The function is f(x) = 3x - 2√x.

Differentiate with respect to x.

(d/dx)f(x) = (d/dx)[3x - 2√x]

f'(x) = (d/dx)(3x) - (d/dx)(2√x)

f'(x) = 3 - 2/2√x

f'(x) = 3 - 1/√x

Answer 2

(2).

The function is f(x) = sin^-1(x) - 1/x +√(2x - 1).

Differentiate with respect to x.

f'(x) = (d/dx)[sin^-1(x) - 1/x +√(2x - 1)]

f'(x) = (d/dx)[sin^-1(x)] - (d/dx)(1/x) +(d/dx)√(2x - 1)

f'(x) = (d/dx)[sin^-1(x)] - (d/dx)(1/x) + [2/2√(2x - 1)]

f'(x) = 1/√(1-x²) + 1/x² +1/√(2x - 1)

 

Answer 3

(3).

The function is f(x) =√[1 + (ln x)²].

Differentiate with respect to x.

f'(x) = (d/dx)√[1 + (ln x)²]

f'(x) = {1/2√[1 + (ln x)²]}*(d/dx)[1 + (ln x)²]

f'(x) = {1/2√[1 + (ln x)²]}*[2(ln x)/x]

f'(x) = ln(x)/x√[1 + (ln x)²]