Find the Derivative - d/dx y=(3x^5-7x^2-4)/(x^2)

Problem

d()/d(x)(3*x^5−7*x^2−4)/(x^2)

Solution

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

y=(3*x^5)/(x^2)−(7*x^2)/(x^2)−4/(x^2)

2. Simplify the terms using the laws of exponents.

y=3*x^3−7−4*x^(−2)

3. Apply the power rule, which states d(x^n)/d(x)=n*x^(n−1) to each individual term.

d(y)/d(x)=(d(3)*x^3)/d(x)−d(7)/d(x)−(d(4)*x^(−2))/d(x)

4. Calculate the derivative of each part.

d(y)/d(x)=9*x^2−0−(−8*x^(−3))

5. Simplify the signs and rewrite the negative exponent as a fraction.

d(y)/d(x)=9*x^2+8/(x^3)

Final Answer

d()/d(x)(3*x^5−7*x^2−4)/(x^2)=9*x^2+8/(x^3)

Want more problems? Check here!