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

1 Answer
Ben
Jul 12, 2018

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)

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