Determine the derivative of the following. Simplify fully.

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Homework Help Overview

The problem involves finding the derivative of the function y = (3x+2)(x+5)^4, which falls under the subject area of calculus, specifically differentiation using the product and chain rules.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the chain rule and product rule but expresses difficulty in progressing beyond a certain point. Other participants suggest factoring and simplifying the expression to aid in the differentiation process.

Discussion Status

The discussion has seen some productive exchanges, with participants offering guidance on factoring and simplifying the expression. However, there is no explicit consensus on the final outcome, as the original poster's attempts and subsequent responses indicate ongoing exploration of the problem.

Contextual Notes

The original poster's approach to using the chain and product rules suggests a focus on standard differentiation techniques, but there may be constraints related to the completeness of their initial attempts and understanding of the simplification process.

1irishman
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Homework Statement



y = (3x+2)(x+5)^4

Homework Equations



Here, i tried using the chain rule on (x+5)^4 first, and then i tried using the product rule
for the entire expression with no success. Can someone help me please?



The Attempt at a Solution



dy/dx (3x+2)(x+5)^4 + dy/dx(x+5)^4(3x+2)
= (3)(x+5)^4 + 4(x+5)^3(3x+2)
=3(x+5)^4 + 4(x+5)^3(3x+2) this is as far as i could go.
 
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Factor out (x+5)3 and simplify the remaining expression.
 
= (x+5)^3(3(x+5) + 4(3x+2))
= (x+5)^3(3x+15 +12X + 8)
dy/dx = (x+5)^3(15x+23) final answer thank u for helping!
 
Last edited:
You're very welcome.

Sam
 

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