JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

\left( {x + y} \right)\sin u = {x^2}{y^2},

then

x\frac{{\partial u}}{{\partial x}} + y\frac{{\partial u}}{{\partial y}}

is equal to

View answer and explanation

Correct option: D

3\tan u

Option D (

3\tan u

) is correct because, by applying Euler's theorem for homogeneous functions, the expression

x\frac{{\partial u}}{{\partial x}} + y\frac{{\partial u}}{{\partial y}}

simplifies to

3\tan u

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