Final answer:
To find the derivative dy/dx of the function y = x³ + 7x + 2/x², apply the power rule to each term resulting in dy/dx = 3x² + 7 - 4/x³.
Step-by-step explanation:
The question asks to find the derivative of the function y = x³ + 7x + 2/x² with respect to x. This is a problem of differentiation, which is a fundamental concept in calculus. The function here is a combination of polynomial terms and a rational term.
Steps to differentiate the function:
- Apply the power rule to differentiate x³ which gives 3x².
- The derivative of 7x with respect to x is 7.
- For the term 2/x², we rewrite it as 2x^-2 and apply the power rule, resulting in -4x^-3 or -4/x³.
Combining these results, the derivative of the given function is dy/dx = 3x² + 7 - 4/x³.