Question
Asked Oct 11, 2019
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Can you show me the steps to solve this problem?

Directions: Find dy/dx by implicit differentiation.

17) √xy = 1 + x2y

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Expert Answer

Step 1

Differentiate both sides with respect to x,

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xy=1+x'y ()(xy) d Since d 1 (uv)=u- (v)+v dx dx 2Vx dy dy 0+2xy x2 1 y +x= 2xy

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Step 2

Multiply the brackets and collect the terms with dy/dx on one side,

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dy dy 2xy+x 1 21y dx dx 2 x dy dy 1 1 -x2 =2xy- 2 Vy dr dx 2 Y x dy = 2.xy- dx 1 1 21 y 1 y 2xy 2 Vx dy 21y श्रीचा शचा शडा करेॐे

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Step 3

Simplify the term on Right hand side. Multiply the numerator with sqrt(x)and...

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4ху — dy x dx х - 2r2 y 4ху — xy 2x - 2r2 4x2y-ay (ху — 2xу x

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Math

Calculus