Question

Please solve this correct ....I will mark the correct answer as brainliest and thank him / her .... question is given in the attachment​

Answer 1

Step-by-step explanation:

2.(a).

We have,

$y = (3x + 8)^{ \frac{7}{3} } (x + 7)^{ - 3}$

$\implies ln(y) = \frac{7}{3} ln(3x + 8) - 3 ln(x + 7)$

Differentiating both sides w.r.t x , we have,

$\implies \frac{1}{y} \frac{dy}{dx} = \frac{7}{3(3x + 8)} - \frac{3}{x + 7}$

$\implies \frac{dy}{dx} = y( \frac{21(x + 7) - 9(3x +8 )}{3(3x + 8)(x + 7)} )$

$\implies \frac{dy}{dx} = y. \frac{21x + 147 - 27x - 72}{3(3x + 8)(x + 7)}$

$\implies \frac{dy}{dx} = y. \frac{( - 2x + 25)}{(3x + 8)(x + 7)}$

$\implies \frac{dy}{dx} = (3x + 8)^{ \frac{7}{3} } (x + 7)^{ - 3} \times \frac{( - 2x + 25)}{(3x + 8)(x + 7)}$

$\implies \frac{dy}{dx} = - (3x + 8)^{ \frac{4}{3} } (x + 7)^{ - 4}( 2x - 25)$