Question

Question #4b9aa

Answer 1

`y^' = -12x^3 - 4x^-3 + 1`

Explanation:

Use the power rule, which states:

If
`f(x) = x^a`
Then
`f'(x) = ax^(a-1)`

Each term can be derived separately since they are added together.

For the first term,
`-3x^4`
The derivative would be
`-3 * (4) x^(4-1)`
which is equivalent to
`-12x^3`

For the second term,
`2x^-2`
The power rule does not change even though the power is negative.
The derivative would be
`2 * (-2) x ^ (-2 - 1)`
which is equivalent to
`-4x^-3`

For the next term,
`x`
which is the same as
`x^1`
The derivative would be
`(1)x^(1-1)`
which is equivalent to
`1x^0`
which is simplified to be
`1`

For the final term,
`-2`
which is equivalent to
`-2 * x^0`
The derivative would be
`-2 * (0) x^(0-1)`
Since it is multiplied by `0`, the entire term is equal to
`0`

Now, since we know all the derivatives, we can add them together.

`-12x^3 + -4x^-3 +1 + 0`

Which simplifies to

`-12x^3 - 4x^-3 + 1`

Answer 2

`dy/dx=-12x^3-4x^-3+1`

Explanation:

`"differentiate each term using the "color(blue)"power rule"`

`•color(white)(x)d/dx(ax^n)=nax^(n-1)`

`y=-3x^4+2x^-2+x-2`

`rArrdy/dx=(-3xx4)x^3+(2xx-2)x^-3+1-0`

`color(white)(rArrdy/dx)=-12x^3-4x^-3+1`