Put the following steps in the correct order for finding the derivative using th

Question

Put the following steps in the correct order for finding the derivative using the chain rule for the function: f(x) = (5x3 + 1)8 (4x5 + 3)7 ____ Fifth Step ____ Second Step ____ First Step ____ Third Step ____ Fourth Step ____ Original function 1. 20x2 (5x3 + 1)7 (4x5 + 3)6 (59x5 + 7x2 + 18) 2. 20x2 (5x3 + 1)7 (4x5 + 3)6 [ 35x5 + 7x2 + 24x5 + 18] 3. 20x2 (5x3 + 1)7 (4x5 + 3)6 [7x2 (5x3 + 1) + 6(4x5 + 3)] 4. 140x4(5x3 + 1)8 (4x5 + 3)6 + 120x2 (4x5 + 3)7 (5x3 + 1)7 5. (5x3 + 1)8 * 7(4x5 + 3)6 (20x4) + (4x5 + 3)7 * 8(5x3 + 1)7 (15x2) 6. (5x3 + 1)8 (4x5 + 3)7 7. (5x3 + 1)8 (4x5 + 3)7 8. (5x3 + 1)8 * 7(4x5 + 3)6 (20x4) + (4x5 + 3)7 * 8(5x3 + 1)7 (15x2) 9. 140x4(5x3 + 1)8 (4x5 + 3)6 + 120x2 (4x5 + 3)7 (5x3 + 1)7 10. 20x2 (5x3 + 1)7 (4x5 + 3)6 [7x2 (5x3 + 1) + 6(4x5 + 3)] 11. 20x2 (5x3 + 1)7 (4x5 + 3)6 [ 35x5 + 7x2 + 24x5 + 18] 12. 20x2 (5x3 + 1)7 (4x5 + 3)6 (59x5 + 7x2 + 18)

Explanation / Answer

f(x) = (5x^3 + 1)^8 (4x^5 + 3)^7 1. 20x2 (5x3 + 1)7 (4x5 + 3)6 (59x5 + 7x2 + 18) 2. 20x2 (5x3 + 1)7 (4x5 + 3)6 [ 35x5 + 7x2 + 24x5 + 18] 3. 20x2 (5x3 + 1)7 (4x5 + 3)6 [7x2 (5x3 + 1) + 6(4x5 + 3)] 4. 140x4(5x3 + 1)8 (4x5 + 3)6 + 120x2 (4x5 + 3)7 (5x3 + 1)7 5. (5x3 + 1)8 * 7(4x5 + 3)6 (20x4) + (4x5 + 3)7 * 8(5x3 + 1)7 (15x2) 6. (5x3 + 1)8 (4x5 + 3)7 7. (5x3 + 1)8 (4x5 + 3)7 8. (5x3 + 1)8 * 7(4x5 + 3)6 (20x4) + (4x5 + 3)7 * 8(5x3 + 1)7 (15x2) 9. 140x4(5x3 + 1)8 (4x5 + 3)6 + 120x2 (4x5 + 3)7 (5x3 + 1)7 10. 20x2 (5x3 + 1)7 (4x5 + 3)6 [7x2 (5x3 + 1) + 6(4x5 + 3)] 11. 20x2 (5x3 + 1)7 (4x5 + 3)6 [ 35x5 + 7x2 + 24x5 + 18] 12. 20x2 (5x3 + 1)7 (4x5 + 3)6 (59x5 + 7x2 + 18) correct order is (6=7)-(5=8)-(4=9)-(3=10)-(2=11)-(1=12)

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