Question

y = (5 ^ x)/(x ^ 5), Find * (dy)/(dx)​

Answer 1

Given: y = 5^x/x⁵

Need to find: We are asked to find d/dx with respect to y.

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¤ To calculate dy/dx, Let's use Quotient rule, It is given by –

$\begin{gathered}\quad\star\;\underline{\boxed{\pmb{\frak{ \sf{}\dfrac{d}{dx}\left(\dfrac{u}{v} \right)= \dfrac{v \times \frac{d}{dx}(u ) - u \times \frac{d}{dx} (v)}{{v}^{2}} }}}}\\\\\end{gathered}$

⠀⠀⠀$\begin{gathered}\underline{\bf{\dag} \:\mathfrak{Substituting\;values\;in\; formula\: :}}\\\\\end{gathered}$

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$\begin{gathered}:\implies\sf \frac{{x}^{5} \dfrac{d}{dx} ( {5}^{x}) - {5}^{x} \frac{d}{dx} ( {x}^{5})}{ {({x}^{5} )}^{2} } \\\\\\:\implies\sf\dfrac{{x}^{5} ( {5}^{x} ln(5))- {5}^{x} ( {5x}^{5 - 1} )}{ {({x}^{5} )}^{2} }\\\\\\:\implies\sf \dfrac{ln(x) \times {5}^{x} {x}^{5} - {5}^{x + 1} \times {x}^{4} }{ {({x}^{5} )}^{2} }\\\\\\:\implies\sf\dfrac{ {5}^{ x } {x}^{4} (ln(5)x - 5)}{ {{x}^{10}}} \\ \\ \\ : \implies \sf \dfrac{ {5}^{ x } \cancel{ {x}^{4} }(ln(5)x - 5)}{ \cancel{{{x}^{10}}}}\\ \\ \\:\implies\underline{\boxed{\pmb{\frak{\dfrac{ {5}^{ x } (ln(5)x - 5)}{ {{x}^{6}}}}}}}\;\bigstar\\\\\end{gathered}$

$\:\;\therefore{\underline{\sf{d/dx \: \: \: of \: \: \: \dfrac{{5}^{x}}{{x}^{5}}\: \: \: is \: \: \: \dfrac{ {5}^{ x } (ln(5)x - 5)}{ {{x}^{6}}}}}}$

Answer 2

Answer:

$46 \times 12 \\ ( - \div 12 \\ \cos(a)$

this is answer