Find the derivative of the function \( h(x)=\left(6 x^{2}+7 x\right)^{5} \)

To find the derivative of the function \( h(x) = (6x^2 + 7x)^5 \), we can use the chain rule. The chain rule states that if you have a composite function \( f(g(x)) \), the derivative is \( f'(g(x)) \cdot g'(x) \). In this case, let \( u = 6x^2 + 7x \), then \( h(x) = u^5 \). First, we find the derivative of \( u \): \[ u' = \frac{d}{dx}(6x^2 + 7x) = 12x + 7. \] Next, find the derivative of \( h \) with respect to \( u \): \[ h' = \frac{d}{du}(u^5) = 5u^4. \] Now, applying the chain rule: \[ h'(x) = h'(u) \cdot u' = 5u^4 \cdot (12x + 7). \] Substituting back \( u = 6x^2 + 7x \): \[ h'(x) = 5(6x^2 + 7x)^4 \cdot (12x + 7). \] Therefore, the derivative is: \[ h'(x) = 5(6x^2 + 7x)^4(12x + 7). \]