Answer:
the derivatives of (u) and (v):(\frac{du}{dx} = \frac{d}{dx}((6x^4 + 3)^5)) using the chain rule.(\frac{dv}{dx} = \frac{d}{dx}(6x^4 +
Explanation:
To find the derivative (f'(x)) of the function (f(x) = \log_7(6x^4 + 3)^5), we can apply the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.Given (f(x) = \log_7(6x^4 + 3)^5), let's break it down into its components:Outer function: (u = \log_7(u)), where (u = (6x^4 + 3)^5).Inner function: (v = 6x^4 + 3).Now, we can find the derivatives of (u) and (v):(\frac{du}{dx} = \frac{d}{dx}((6x^4 + 3)^5)) using the chain rule.(\frac{dv}{dx} = \frac{d}{dx}(6x^4 +