Question #4b9aa
2 Answers
Explanation:
Use the power rule, which states:
If
Then
Each term can be derived separately since they are added together.
For the first term,
The derivative would be
which is equivalent to
For the second term,
The power rule does not change even though the power is negative.
The derivative would be
which is equivalent to
For the next term,
which is the same as
The derivative would be
which is equivalent to
which is simplified to be
For the final term,
which is equivalent to
The derivative would be
Since it is multiplied by
Now, since we know all the derivatives, we can add them together.
Which simplifies to
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#