power rule

Question

log3xp

Answer 1

To differentiate the expression using the power rule, we differentiate each term separately.

The power rule states that d/dx(x^n) = nx^(n-1), where n is a constant.

In this case, we have:

d/dx(log(3xp))

= d/dx(log(3x) + log(p))

Using the power rule, we differentiate each term separately:

= d/dx(log(3x)) + d/dx(log(p))

Applying the derivative of the logarithmic function, we have:

= 1/(3x) * d/dx (3x) + 1/p * d/dx (p)

= 1/(3x) * 3 + 0

= 1/x

Therefore, the derivative of log(3xp) with respect to x is 1/x.