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  • Differentiate each of the functions w.r. to x in (2x – 7)2 (3x + 5)3

Differentiate each of the functions w.r. to x in

(2x - 7)^{2} (3x + 5)^{3}

Answers (1)

This question will involve the concept of both chain rule and product rule

Given that y= \left( 2x-7 \right) ^{2} \left( 3x+5 \right) ^{3}~ \\ \\

Applying product rule of differentiation
  \\ \frac{dy}{dx}= \left( 3x+5 \right) ^{3}\frac{d}{dx} \left( 2x-7 \right) ^{2}+ \left( 2x-7 \right) ^{2}\frac{d}{dx} \left( 3x+5 \right) ^{3} \\ \\ = \left( 3x+5 \right) ^{3} *2 * \left( 2x-7 \right) *2+ \left( 2x-7 \right) ^{2} *3 * \left( 3x+5 \right) ^{2} *3 \\ \\ = \left( 2x-7 \right) \left( 3x+5 \right) ^{2} \left[ 4 \left( 3x+5 \right) +9 \left( 2x-7 \right) \right] \\ \\ = \left( 2x-7 \right) \left( 3x+5 \right) ^{2} \left( 30x-43 \right) \\ \\

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infoexpert21

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