Question

Find the derivatives of the following using the different rules.1. f(x) = 722. f(x) = -67x

Answer 1

Answer:

• (a)f'(x)=0

,

• (b)f'(x)=-67

Explanation:

(a)Given the function:

$f(x)=72$

By the rules of differentiation given below:

$\begin{gathered} \frac{d}{dx}(c)=0 \\ where\text{ c is a constant.} \end{gathered}$

Therefore:

$\begin{gathered} \frac{d}{dx}(72)=0 \\ f^{\prime}(x)=0 \end{gathered}$

(b) Given the function:

$f\mleft(x\mright)=-67x$

Using the rule of derivatives below:

$\frac{d}{dx}[cf(x)]=c\frac{d}{dx}[f(x)],c\text{ a constant}$

Applying this rule:

$\begin{gathered} \frac{d}{dx}[-67x]=-67\frac{d}{dx}[x] \\ =-67(1) \\ \implies f^{\prime}(x)=-67 \end{gathered}$

The derivative is -67.