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

1 Answer
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)#