Question

How do you find the derivative of the function `f(x)=-2x^-3+x^2-7`?

Answer 1

`(df)/(dx) = 6x^(-4)+2x`

Explanation:

The derivative of a sum of terms is equal to the sum of the derivatives of the individual terms:

`(d(-2x^3+x^2-7))/(dx) = (d(-2x^-3))/(dx)+(d(x^2))/(dx)+(d(-7))/(dx)`

The derivative (with respect to `x`) of `a*x^b` is
`color(white)("XXXX")(d (ax^b))/(dx) = b*ax^(-1)`

So
`color(white)("XXXX")(d(-2x^(-3)))/(dx) = (-3) *(-2)x^(-4) = 6x^(-4)`

`color(white)("XXXX")(d(x^2))/(dx) = (2) * (1)x^1 = 2x`

`color(white)("XXXX")(d (-7))/(dx) = (d (-7x^0))/(dx) = (0) * (-7)x^(-1) = 0`