Find the Derivative - d/dx (x^5)/(x^3)

Problem

d()/d(x)(x^5)/(x^3)

Solution

1. Simplify the expression before differentiating by using the quotient rule for exponents, which states that (x^a)/(x^b)=x^(a−b)

(x^5)/(x^3)=x^(5−3)

(x^5)/(x^3)=x^2

2. Apply the power rule for derivatives, which states that d(x^n)/d(x)=n*x^(n−1)

d(x^2)/d(x)=2*x^(2−1)

3. Simplify the resulting exponent.

2*x^1=2*x

Final Answer

d()/d(x)(x^5)/(x^3)=2*x

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