Find the Derivative - d/dx (x^3-3x^2+10x-5)/(x^2)

Problem

d()/d(x)(x^3−3*x^2+10*x−5)/(x^2)

Solution

1. Simplify the expression by dividing each term in the numerator by the denominator x^2

(x^3−3*x^2+10*x−5)/(x^2)=(x^3)/(x^2)−(3*x^2)/(x^2)+(10*x)/(x^2)−5/(x^2)

2. Rewrite the terms using power notation to make differentiation easier.

x−3+10*x^(−1)−5*x^(−2)

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

d(x)/d(x)−d(3)/d(x)+(d(10)*x^(−1))/d(x)−(d(5)*x^(−2))/d(x)

4. Calculate the derivative of each term.

1−0+(−10*x^(−2))−(−10*x^(−3))

5. Simplify the signs and rewrite the expression with positive exponents.

1−10/(x^2)+10/(x^3)

Final Answer

d()/d(x)(x^3−3*x^2+10*x−5)/(x^2)=1−10/(x^2)+10/(x^3)

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