Find the Derivative - d/dx (x^5)/10

Problem

d()/d(x)(x5)/10

Solution

1. Identify the constant factor in the expression. The expression (x5)/10 can be rewritten as 1/10⋅x5

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

d()/d(x)(x5)/10=1/10⋅d(x5)/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) where n=5

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

4. Substitute the result back into the expression and simplify the fraction.

1/10⋅5*x4=5/10*x4

5. Simplify the coefficient by dividing both the numerator and denominator by 5.

5/10*x4=1/2*x4

Final Answer

d()/d(x)(x5)/10=(x4)/2

Want more problems? Check here!