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

Problem

d()/d(x)(x3−3*x2+10*x−5)/(x2)

Solution

1. Simplify the expression by dividing each term in the numerator by the denominator x2

(x3−3*x2+10*x−5)/(x2)=(x3)/(x2)−(3*x2)/(x2)+(10*x)/(x2)−5/(x2)

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(xn)/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/(x2)+10/(x3)

Final Answer

d()/d(x)(x3−3*x2+10*x−5)/(x2)=1−10/(x2)+10/(x3)

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