Differentiate the following functions. (2x-7)^ 2 (3x+5)^ 3 - Vidyadip

Question

Differentiate the following functions.
$(2\text{x}-7)^{2}(3\text{x}+5)^{3}$

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Answer

$\frac{\text{d}}{\text{dx}}(2\text{x}-7)^{2}(3\text{x}+5)^{3}$
$=(2\text{x}-7^{2}).\frac{\text{d}}{\text{dx}}(3\text{x}+5)^{3}+(3\text{x}+5)^{3}.\frac{\text{d}}{\text{dx}}(2\text{x}-7)^{2}$
[Using product Rule]
⇒ (2x - 7)².3(3x + 5)².3 + (3x + 5)³.2(2x - 7).2
⇒ 9(2x - 7)²(3x + 5)²[9(2x) - 7) + 4(3x + 5)]
⇒ (2x - 7)(3x - 5)²(18 - 63 + 12x + 20)
⇒ (2x - 7)(3x + 5)²(30x - 43)
Hence, the required answer is (2x - 7)(30x - 43)(3x + 5)².

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