Differentiate the given function. \( F(t)=\left(9 t+\frac{3}{t}\right)\left(3 t^{2}-7\right) \)

Find the first order derivative with respect to \( t \) for \( (9t+3/t)*(3t^2-7) \). Evaluate the derivative by following steps: - step0: Evaluate the derivative: \(\frac{d}{dt}\left(\left(9t+\frac{3}{t}\right)\left(3t^{2}-7\right)\right)\) - step1: Add the terms: \(\frac{d}{dt}\left(\frac{9t^{2}+3}{t}\times \left(3t^{2}-7\right)\right)\) - step2: Multiply the terms: \(\frac{d}{dt}\left(\frac{\left(9t^{2}+3\right)\left(3t^{2}-7\right)}{t}\right)\) - step3: Simplify: \(\frac{d}{dt}\left(\frac{27t^{4}-54t^{2}-21}{t}\right)\) - step4: Use differentiation rules: \(\frac{\frac{d}{dt}\left(27t^{4}-54t^{2}-21\right)\times t-\left(27t^{4}-54t^{2}-21\right)\times \frac{d}{dt}\left(t\right)}{t^{2}}\) - step5: Calculate: \(\frac{\left(108t^{3}-108t\right)t-\left(27t^{4}-54t^{2}-21\right)\times 1}{t^{2}}\) - step6: Calculate: \(\frac{t\left(108t^{3}-108t\right)-\left(27t^{4}-54t^{2}-21\right)}{t^{2}}\) - step7: Calculate: \(\frac{81t^{4}-54t^{2}+21}{t^{2}}\) The first derivative of the function \( F(t)=\left(9 t+\frac{3}{t}\right)\left(3 t^{2}-7\right) \) with respect to \( t \) is \( \frac{81t^{4}-54t^{2}+21}{t^{2}} \).