Question

if 3axy=c then Dy /DX=?

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Answer 1

SOLUTION

GIVEN

$\sf{3axy = c}$

TO DETERMINE

$\displaystyle \sf{ \frac{dy}{dx} }$

EVALUATION

Here it is given that

$\displaystyle \sf{3axy = c }$

$\displaystyle \sf{ \implies \: y = \frac{c}{3ax} }$

$\displaystyle \sf{ \implies \: y = \frac{c}{3a} \: {x}^{ - 1} }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = \frac{d}{dx} \bigg(\frac{c}{3a} \: {x}^{ - 1} \bigg)}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = \frac{c}{3a} \times \frac{d}{dx} \bigg( \: {x}^{ - 1} \bigg)}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = \frac{c}{3a} \times ( - 1) \: {x}^{ - 1 - 1} }$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = - \frac{c}{3a} \: {x}^{ - 2} }$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = - \frac{c}{3a {x}^{2} } \: }$

FINAL ANSWER

$\displaystyle \sf{ \: \frac{dy}{dx} = - \frac{c}{3a {x}^{2} } \: }$

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