if xa5+yb5=5, then dydxat(a,b) is

if ${[\frac{x}{a}]}^{5} + {[\frac{y}{b}]}^{5} = 5$ , then ${\frac{d y}{d x}}_{at (a, b)}$ is

A
$\frac{α}{b}$
B
$\frac{- a}{b}$
C
$\frac{b}{a}$
D
$\frac{- b}{a}$

Solution:

$5. {[\frac{x}{a}]}^{4} \frac{1}{a} + 5 {[\frac{y}{b}]}^{4} \frac{1}{b} . y^{1} = 0$

$5 \frac{y^{1}}{b} . \frac{y^{4}}{b^{4}} = \frac{- 5}{a} . \frac{x^{4}}{a^{4}}$

${\frac{d y}{d x}}_{_{(a, b)}} = y^{1} = \frac{- b^{5} a^{4}}{a^{5} b^{4}} = \frac{- b}{a}$

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