find the derivative of the function?

Question

y=x^4 -2
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x

Answer 1

If you mean (x^4 - 2)/x, isn't it easier to just write it like that, instead of trying to draw the fraction bar?

Split it into two fractions: x^4/x - 2/x.
The derivative of x^4/x=x^3 is 3x^2.
The derivative of -2/x is 2/x^2.

The final answer is 3x^2+2/x^2 or (3x^4 + 2)/x^2.

Alternatively, you can use the quotient rule.
f= x^4-2 and g=x
The derivative of f/g is (f'g - g'f)/g^2.
f'=4x^3
g'=1
f'g=(4x^3)(x)=4x^4
g'f=(1)(x^4-2)=x^4-2
f'g-g'f= 4x^4-(x^4-2)=4x^4-x^4+2=3x^4+2
The final answer (as above) is (3x^4+2)/x^2.

Answer 2

y = (x^4 - 2)/x

y' = (x(x^4 - 2)' - x'(x^4 - 2))/(x^2)
y' = (x(4x^3) - (x^4 - 2))/(x^2)
y' = (4x^4 - x^4 + 2)/(x^2)
y' = (3x^4 + 2)/(x^2)

Answer 3

y'=4X^3