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Sagot :
Answer:
[tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]
Step-by-step explanation:
Explanation
Given function f(r) = r² log r ....(i)
Apply derivatives formula
[tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]
[tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]
[tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]
Differentiating equation (i) with respective to 'r' , we get
[tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]
[tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]
Final answer:-
[tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]
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