If xlog, (log, x) = x2 + y2 + 4(y >...
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If xlog, (log, x) = x2 + y2 + 4(y > 0), then dy at x = e is equal to X qual to (26-1) (1 + 2e) (2) 214+e? (4) JA+e?

JEE/Engineering Exams
Maths
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at ( x=e, ) ( e log _{e}left(log _{e} eright)-e^{2}+y^{2}=4 ) ( Rightarrow quad y^{2}=4+e^{2} Rightarrow y=sqrt{4+e^{2}} ) ( quad x log _{e}left(log _{e} xright)-x^{2}+y^{2}=4 ) ( Rightarrow log _{e}left(log _{e} xright)+frac{x}{log _{e} x frac{1}{x}}-2 x+2 y frac{d y}{d x}=0 ) ( Rightarrow quad log _{e}left(log _{e} xright)+frac{1}{log _{e} x}-2 x+2 y frac{d y}{d x}=0 ) dt ( x=e ) ( Rightarrow log _{e}left(log _{e} eright)+frac{1}{log _{e} e}-2 e+2 sqrt{4+e^{2}} frac{d y}{d t}=0 ) ( Rightarrow frac{1}{1}-2 e+2 sqrt{4+e^{2}} frac{d y}{d x}=0 ) ( Rightarrow quad 2 cdot sqrt{4+e^{2}} frac{d y}{d x}=2 e-1 ) ( Rightarrow frac{d y}{d x}=frac{2 e-1}{2 sqrt{4+e^{2}}} ) Ophon
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