Question

$\large{ \boxed{ \bold \red{\frac{d}{dx} \: \frac{\frac{3}{5}{x}^{2}-\frac{1}{2}}{\frac{5}{6}xy+8{y}^{2}}}}}$

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Answer 1

$\bold \red{\frac{d}{dx} \: \frac{\frac{3}{5}{x}^{2}-\frac{1}{2}}{\frac{5}{6}xy+8{y}^{2}}}$

${ \bold \red{\frac{d}{dx} \frac{\frac{3{x}^{2}}{5}-\frac{1}{2}}{\frac{5}{6}xy+8{y}^{2}}}}$

${ \bold \red{\frac{d}{dx} \frac{\frac{3{x}^{2}}{5}-\frac{1}{2}}{\frac{5xy}{6}+8{y}^{2}}}}$

$\bold \red{\frac{d}{dx} \frac{3{x}^{2}\times 2-5}{5\times 2}\times \frac{6}{5xy+8{y}^{2}\times 6}}$

$\bold \red{\frac{d}{dx} \frac{6{x}^{2}-5}{10}\times \frac{6}{5xy+8{y}^{2}\times 6}}$

$\bold \red{\frac{d}{dx} \frac{(6{x}^{2}-5)\times 6}{10(5xy+48{y}^{2})}}$

$\bold \red{ \frac{d}{dx} \frac{6(6{x}^{2}-5)}{10(5xy+48{y}^{2})}}$

$\bold \red{ \frac{d}{dx} \frac{3(6{x}^{2}-5)}{5(5xy+48{y}^{2})}}$

$\bold \red{ \frac{3}{5}(\frac{d}{dx} \frac{6{x}^{2}-5}{5xy+48{y}^{2}})}$

${\bold \red{\frac{3}{5}\times \frac{(5xy+48{y}^{2})(\frac{d}{dx} 6{x}^{2}-5)-(6{x}^{2}-5)(\frac{d}{dx} 5xy+48{y}^{2})}{{(5xy+48{y}^{2})}^{2}}}}$

${ \bold \red{ \frac{3}{5}\times \frac{12x(5xy+48{y}^{2})-(6{x}^{2}-5)(\frac{d}{dx} 5xy+48{y}^{2})}{{(5xy+48{y}^{2})}^{2}}}}$

${ \bold \red{ \frac{3}{5}\times \frac{12x(5xy+48{y}^{2})-(6{x}^{2}-5)((\frac{d}{dx} 5xy)+(\frac{d}{dx} 48{y}^{2}))}{{(5xy+48{y}^{2})}^{2}}}}$

$\bold \red{\frac{3(30{x}^{2}y+576x{y}^{2}+25y)}{5{(5xy+48{y}^{2})}^{2}}}$