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!
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 )
--------------------------------------…
The second one:
-------------------------
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 )
---------------------
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 )
--------------------------------------…
The second one:
-------------------------
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 )
-
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)
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)