Question

If y = e^{log x} then `dy/dx` = ______.

विकल्प

• `1/x`

• `1/2`

• `e^(log x)/x`

• 0

Answer 1

If y = e^{log x} then `dy/dx` = `underlinebb(e^(log x)/x)`.

Explanation:

Applying the chain rule to y = e^u where u = log x:

`dy/dx = e^(log x) * d/dx (log x)`

= `e^(log x) * 1/x`

= `e^(log x)/x`

Since e^{log x} = x, this expression simplifies to `x/x = 1`, making it mathematically equivalent to the simplified result.