find the derivative of the given equation: $f(x)=-4x$
find the derivative of the given equation: $f(x)=-4x$
Answer
Explanation:
Step1: Apply the power rule
The power rule states that if ( f(x)=ax^n ), then ( f^\prime(x)=nax^{n - 1} ). For ( f(x)=-4x=-4x^1 ), here ( a=-4 ) and ( n = 1 ).
Step2: Calculate the derivative
Using the power rule: ( f^\prime(x)=1\times(-4)x^{1-1}=-4x^0 ). Since ( x^0 = 1) (for ( x\neq0), and in the context of derivatives of polynomial - like functions, we consider the general form), so ( f^\prime(x)=-4).
Answer:
( f^\prime(x)=-4 ) (the fourth option)