Question

If f(x) = sin(ln(2x)), then f’(x)=

Answer 1

B. cos(ln(2x))/x

Explanation:

We know that the inverse of sin is cosine. Note, arcsin means the same thing as inverse sin:

• sin(ln(2x))

Because sin (a) = sin (b) --> a = arcsin (b)

• Therefore: ln(2x) = arcsin(y)
• Solve ln(2x)=arcsin(y) for x
• (e^arcsin(y))/2

Subsitute y = x

• (e^arcsin(x))/2
• Therefore, we get the answer as cos(ln(2x))/x