Question

Find the derivatives of the following using the different rules.1. f(x) = -67x

Answer 1

To derive f(x) = -67x, we can use the Power Rule.

`x^n\Rightarrow nx^(n-1)`

In the given term, our n = 1 since x¹ = x. So, following the power rule, we will multiply the exponent 1 to the constant term -67, then subtract 1 from the exponent 1, hence x¹ will become x⁰.

`-67x^1\Rightarrow1(-67)(x^(1-1))`

Then, simplify.

`-67x^0\Rightarrow-67(1)=-67`

Therefore, the first derivative of f(x) = -67x is -67.

`f^(\prime)(x)=-67`