Question

How do you find the derivative of `g(t)=t^-3`?

Answer 1

Use the same method as if the exponent was positive: Multiply the function by the current exponent, and raise the variable to `n-1` exponent: `g'(t)=-3t^(-4)`

Explanation:

For a given function `f(x)` with an exponent:

`f(x)=x^n`

The derivative comes out to:

`f'(x)=nx^(n-1)`

Apply this to the function in question:

`g(t)=t^(-3)`

`g'(t)=-3t^(-3-1)`

`color(green)(g'(t)=-3t^-4)`