Find the Derivative - d/dx y=(x^5+7)/(x^3)

Problem

d()/d(x)(x5+7)/(x3)

Solution

1. Simplify the expression by dividing each term in the numerator by the denominator to avoid using the quotient rule.

y=(x5)/(x3)+7/(x3)

2. Rewrite the terms using laws of exponents to prepare for the power rule.

y=x2+7*x(−3)

3. Apply the power rule for derivatives, which states d(xn)/d(x)=n*x(n−1) to each term individually.

d(y)/d(x)=2*x(2−1)+7*(−3)*x(−3−1)

4. Simplify the resulting expression by performing the multiplication and subtraction in the exponents.

d(y)/d(x)=2*x−21*x(−4)

5. Convert the negative exponent back into a fraction to match the form of the original problem.

d(y)/d(x)=2*x−21/(x4)

Final Answer

d()/d(x)(x5+7)/(x3)=2*x−21/(x4)

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