Question

power rule

3log 2, 5

Answer 1

[AI-generated answer — Bot GPT 3.5]

The power rule states that for any real number n and any positive real number b, the derivative of b^n with respect to x is equal to n*b^(n-1) times the derivative of x with respect to x.

Applying the power rule to the expression 3log2(5), we can rewrite it as 3 * (log2(5))^1.

Taking the derivative of (log2(5))^1 with respect to x, we get 1*(log2(5))^(1-1) * derivative of log2(5) with respect to x.

The derivative of log2(5) with respect to x is 1/(x * ln(2)), where ln(2) is the natural logarithm of 2.

Substituting back into the original expression, we have:

3 * (log2(5))^1 * 1/(x * ln(2))

Simplifying, we get:

3 * log2(5) / (x * ln(2))