How to Find the Derivative of a Monomial

Step-by-Step Guide

1. 1

   Step 1: Rewrite the monomial so that it is in the form of f(x)=axn{\displaystyle f(x)=ax^{n}}.

   In this equation, a{\displaystyle a} is a coefficient, and n{\displaystyle n} is the power of x.{\displaystyle x.} For example, the square root x{\displaystyle {\sqrt {x}}} may be rewritten as x1/2.{\displaystyle x^{1/2}.} , This is the well-known power rule, which works for integers, rational numbers, and even real numbers for n.{\displaystyle n.} f′(x)=anxn−1{\displaystyle f^{\prime }(x)=anx^{n-1}} ,, f′(x)=5⋅8x7=40x7{\displaystyle f^{\prime }(x)=5\cdot 8x^{7}=40x^{7}} , f(x)=2x4{\displaystyle f(x)=2x^{4}} f(x)=3x2/3{\displaystyle f(x)=3x^{2/3}} f(x)=2x−5{\displaystyle f(x)=2x^{-5}} f(x)=10x1000{\displaystyle f(x)=10x^{1000}}
2. 2

   Step 2: Multiply the entire term by the power of x{\displaystyle x} and subtract one from the exponent.

3. 3

   Step 3: Find the derivative of f(x)=5x8{\displaystyle f(x)=5x^{8}}.

4. 4

   Step 4: Use the power rule.

5. 5

   Step 5: Practice by finding the derivatives of the following monomials.

Detailed Guide

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