Question

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Any maths genius


Class 12.


If y = √x(x+4)^3/2/+(4x-3)^4/3 , find dy/dx ​

Answer 1

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf{GIVEN \colon - }$

$\sf \huge {y = \frac{ \sqrt{x}(x + 4) ^{ \frac{3}{2} } }{(4x - 3) ^{ \frac{4}{3} } } }..(1)$

→ Taking logorithm on both sides of (1), we get

$\sf \: log \: y = \frac{1}{2} \: log \: x + \frac{3}{2} \: log (x + 4) - \frac{4}{3} \\ \sf \: log(4x - 3)$

→ On differentiating both sides w.r.t.x , we get

$\sf \: \frac{1}{y} . \frac{dy}{dx} = \frac{1}{2} . \frac{1}{x} + \frac{3}{2} . \frac{1}{(x + 4)} - \frac{4}{3} . \frac{4}{(4x - 3)}$

$\sf \implies \frac{dy}{dx} = y( \frac{1}{2x} + \frac{3}{2(x + 4)} - \frac{16}{3(4x - 3)} ) \\ \\ \sf \: \frac{ \sqrt{x} (x + 4) ^{ \frac{3}{2} } }{(4x - 3) ^{ \frac{4}{3} } } .( \frac{1}{2x} + \frac{3}{2(x + 4)} - \frac{16}{3(4x - 3)} )$

Answer 2

Answer:

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