Question

What is the derivative of `y = (x^2+4x+3)/sqrtx`?

What is the derivative of `y = (x^2+4x+3) / sqrtx`

Answer 1

`y' =3/2 x^(1/2) + 2x^(-1/2) - 3/2x^(-3/2)`

Explanation:

Step 1: Simply the function
Since `sqrtx` is on the denominator, we can think of it as `x^(-1/2)` and multiply through to the numerator:
`y = (x^2+4x+3)x^(-1/2)`

Step 2: Distribution
After simplifying the original equation, we can now distribute `x^(-1/2)` to the numerator `(x^2 + 4x +3)`. We get `y = x^(3/2)+4x^(1/2)+3x^(-1/2)`

Step 3: Take the derivative
We can see now the function is in its simplest form as `y = x^(3/2)+4x^(1/2)+3x^(-1/2)`. We can take the derivative of each term in the function by applying the power rule. `y' = (3/2)x^(1/2)+(1/2)4x^(-1/2)+(-1/2)3x^(-3/2)` And finally, the answer will be `y' =3/2 x^(1/2) + 2x^(-1/2) - 3/2x^(-3/2)`