What is the first derivative of y= (4x^2 + 2x)/x^2. Can this be done without using the quotient rule.

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that:

y= (4x^2 - 2x) / x^2

We need to find the first derivative y'.

First we will simplify the expression.

We will factor x from the numerator.

==> y= x*(4x + 2) / x^2

Now we will reduce x.

==> y= (4x+2)/x

Now we will rewrite :

==> y= 4x/x + 2/x

==> y= 4 + 2/x

Now we will find the derivative.

==> y' = 0 - 2/x^2

==> y' = -2/x^2

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find the first derivative of y=(4x^2+2x)/x^2. Here it is not necessary to use the quotient rule.

y=(4x^2+2x)/x^2

=> y = 4x^2 / x^2 + 2x / x^2

=> y = 4 + 2/x

=> y = 4 + 2*x^-1

y' = 0 + 2*(-1)*x^(-2)

=> y' = -2*x^(-2)

=> y' = -2 / x^2

The required derivative is -2/x^2

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