Use differentiation to verify each equation.


d/dx (x⁴ − ln(x⁴ + 1))=4x⁷ / (1 + x⁴).

Verified step by step guidance

1. Start by applying the differentiation rules to the left-hand side of the equation, which is d/dx (x⁴ − ln(x⁴ + 1)).
2. Use the power rule to differentiate x⁴, which states that d/dx (x^n) = n*x^(n-1). Thus, the derivative of x⁴ is 4x³.
3. Next, differentiate the term -ln(x⁴ + 1) using the chain rule, which states that d/dx [ln(u)] = (1/u) * (du/dx), where u = x⁴ + 1.
4. Calculate du/dx for u = x⁴ + 1, which is 4x³, and substitute this back into the derivative of the logarithmic term.
5. Combine the results from the differentiation of both terms to form the complete derivative and simplify to verify if it equals the right-hand side, 4x⁷ / (1 + x⁴).