Differentiate. \[ y=\left(9 x^{2}+8\right)(5 x+4) \] \( y^{\prime}=\square \)
Solución de inteligencia artificial de Upstudy
Responder
Solución
Respondido por UpStudy AI y revisado por un tutor profesional


Extra Insights
To differentiate the function \( y = (9x^2 + 8)(5x + 4) \), we can apply the product rule, which states that if you have two functions \( u \) and \( v \), then \( (uv)' = u'v + uv' \). Let: - \( u = 9x^2 + 8 \) - \( v = 5x + 4 \) Now, differentiate each part: - \( u' = 18x \) - \( v' = 5 \) Using the product rule: \[ y' = u'v + uv' = (18x)(5x + 4) + (9x^2 + 8)(5) \] Now, substituting in known values: \[ y' = 18x(5x + 4) + (9x^2 + 8)(5) \] Distributing gives: \[ = 90x^2 + 72x + 45x^2 + 40 \] Combining like terms: \[ y' = 135x^2 + 72x + 40 \] Therefore, the final result is: \[ y' = 135x^2 + 72x + 40 \]
