1. Problem: Differentiate $x^7 \times x^3 \times x^3 \times x^7$. 2. Use the product rule for powers of the same base: $x^a \times x^b = x^{a+b}$. 3. Combine exponents: $7 + 3 + 3 + 7 = 20$, so the function is $x^{20}$. 4. Differentiate using the power rule: $\frac{d}{dx} x^n = n x^{n-1}$. 5. Derivative: $20 x^{19}$. --- 1. Problem: Differentiate $x^4 \times x^5 \times x^5 \times x^4$. 2. Combine exponents: $4 + 5 + 5 + 4 = 18$, so the function is $x^{18}$. 3. Derivative: $18 x^{17}$. --- 1. Problem: Differentiate $x^{10} \times x^2 \times x^2 \times x^{10}$. 2. Combine exponents: $10 + 2 + 2 + 10 = 24$, so the function is $x^{24}$. 3. Derivative: $24 x^{23}$. --- 1. Problem: Differentiate $x^6 \times x^6 \times x^6 \times x^6$. 2. Combine exponents: $6 + 6 + 6 + 6 = 24$, so the function is $x^{24}$. 3. Derivative: $24 x^{23}$. --- 1. Problem: Differentiate $x^8 \times x^4 \times x^4 \times x^8$. 2. Combine exponents: $8 + 4 + 4 + 8 = 24$, so the function is $x^{24}$. 3. Derivative: $24 x^{23}$. --- 1. Problem: Differentiate $x^9 \times x^3 \times x^3 \times x^9$. 2. Combine exponents: $9 + 3 + 3 + 9 = 24$, so the function is $x^{24}$. 3. Derivative: $24 x^{23}$. --- 1. Problem: Differentiate $x^{12} \times x^7 \times x^7 \times x^{12}$. 2. Combine exponents: $12 + 7 + 7 + 12 = 38$, so the function is $x^{38}$. 3. Derivative: $38 x^{37}$. --- 1. Problem: Differentiate $x^5 \times x^1 \times x^1 \times x^5$. 2. Combine exponents: $5 + 1 + 1 + 5 = 12$, so the function is $x^{12}$. 3. Derivative: $12 x^{11}$. --- 1. Problem: Differentiate $x^{11} \times x^5 \times x^5 \times x^{11}$. 2. Combine exponents: $11 + 5 + 5 + 11 = 32$, so the function is $x^{32}$. 3. Derivative: $32 x^{31}$. --- 1. Problem: Differentiate $x^{15} \times x^{10} \times x^{10} \times x^{15}$. 2. Combine exponents: $15 + 10 + 10 + 15 = 50$, so the function is $x^{50}$. 3. Derivative: $50 x^{49}$.