Differentiate the function given below w.r.t. $x :$

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

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Solution

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

Differentiating with respect to $x,$ we get

$= \frac{ⅆ}{ⅆ x} [(2 x - 7)^{2} (3 x + 5)^{3}]$

$= (2 x - 7)^{2} \frac{ⅆ}{ⅆ x} (3 x + 5)^{3}$

$+ (3 x + 5)^{3} \frac{ⅆ}{ⅆ x} (2 x - 7)^{2}$

$= (2 x - 7)^{2} \cdot 3 (3 x + 5)^{2} (3)$

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

$= 9 (2 x - 7)^{2} (3 x + 5)^{2} + 4 (2 x - 7) (3 x + 5)^{3}$

$[∵ \frac{d x^{n}}{d x} = n x^{n - 1}]$

$= (2 x - 7) (3 x + 5)^{2} [9 (2 x - 7) + 4 (3 x + 5)]$

$= (2 x - 7) (3 x + 5)^{2} (30 x - 43)$

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