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EXAMPLE 1 Differentiate y = ln(x^3 + 7). SOLUTION To use the Chain Rule, we let u = x^3 + 7. Then y = ln(u), so dy/dx = dy/du * du/dx = [ ] du/dx = 1 / (x^3 + 7) * ( [ ] ) = (3x^2) / (x^3 + 7)

          EXAMPLE 1 Differentiate y = ln(x^3 + 7).

SOLUTION To use the Chain Rule, we let u = x^3 + 7. Then y = ln(u), so

dy/dx = dy/du * du/dx = [      ] du/dx
= 1 / (x^3 + 7) * ( [      ] )
= (3x^2) / (x^3 + 7)

Added by William W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

07/04/2022

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Step 1:** Let \( u = x^3 + 7 \) ** Show more…

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EXAMPLE 1: Differentiate In(x) SOLUTION: To use the Chain Rule, we let u = x + 7. Then In(u), dy/dx

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EXAMPLE 1 Differentiate y = ln(x^3 + 7). SOLUTION To use the Chain Rule, we let u = x^3 + 7. Then y = ln(u), so dy/dx = dy/du * du/dx = [ ] du/dx = 1 / (x^3 + 7) * ( [ ] ) = (3x^2) / (x^3 + 7)

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