Find the Derivative - d/dx (x^5)/120

Problem

d()/d(x)(x5)/120

Solution

1. Identify the constant factor in the expression. The term (x5)/120 can be rewritten as 1/120⋅x5

2. Apply the constant multiple rule for derivatives, which states that d()/d(x)*[c⋅ƒ(x)]=c⋅d(ƒ(x))/d(x)

3. Apply the power rule to the term x5 The power rule states that d(xn)/d(x)=n*x(n−1)

d(x5)/d(x)=5*x4

4. Multiply the constant factor by the derivative of the power term.

1/120⋅5*x4

5. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5.

5/120=1/24

Final Answer

d()/d(x)(x5)/120=(x4)/24

Want more problems? Check here!