Question

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

Options

• `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:

Option c is correct: 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.

Option a is incorrect: `1/x` is the derivative of log x, not e^{log x}.

Option b is incorrect: `1/2` is a constant and does not relate to the derivative of this variable function.

Option d is incorrect: The derivative is zero only for constant functions; y = e^{log x} changes as x changes.