Very simple brief calculus question
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Very simple brief calculus question

[From: ] [author: ] [Date: 12-07-14] [Hit: ]
........
Hello! My question is Find the derivative of each function defined as follows

Y=(6)/(4√x)

y=6/4√x

Idk how to write it properly .. Thanks for your time fellas!

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The first one:
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Y = (6) / (4√x) we will rewrite the equation to this form

Y = ( 6 / 4 ) * (x^-0.5) then the derivative will be

( dY / dx ) = ( 3 / 2 ) * ( -0.5 * x^-0.5-1)

= - ( 3 / 2 ) * ( 1 / 2 ) * (x^-1.5)

= - ( 3 ) / ( 4 (√x)^3 )
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The second one:
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y = 6/4√x

= ( 3 / 2 ) * (x^0.5)

( dy / dx ) = (3 / 2) * ( 0.5 x^0.5-1)

= ( 3 / 2 ) * ( 1 / 2 ) * (x^-0.5)

= ( 3 / 4 ) * ( (√x)^-1 )

= ( 3 ) / ( 4√x )

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Write it like a power series (of the form ax^n). Then use power rule to solve...

Y = 6/( 4√x )
= 6/4 * x^(-1/2)
dY/dx = 6/4 * -1/2 * x^(-1/2 - 1)
= -3/4 * x^(-3/2)
= -3 / (4x√x)
1
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