If ${x^x}{y^y}{z^z} = c$, then $\frac{{\partial z}}{{\partial x}}$ is equal to

$\left( {\frac{{1 + \log z}}{{1 + \log x}}} \right)$

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

{x^x}{y^y}{z^z} = c

, then

\frac{{\partial z}}{{\partial x}}

is equal to

View answer and explanation

Correct option: B

- \left( {\frac{{1 + \log x}}{{1 + \log z}}} \right)

Option B (

-(\frac{{1 + \log x}}{{1 + \log z}})

) is correct because it is the result of partially differentiating the given equation with respect to x and solving for

\frac{{\partial z}}{{\partial x}}

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