Find the Derivative - d/dx (x^3+x+1)/x

Problem

d()/d(x)(x3+x+1)/x

Solution

1. Simplify the expression by dividing each term in the numerator by the denominator x before differentiating.

(x3+x+1)/x=(x3)/x+x/x+1/x

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

x2+1+x(−1)

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

d(x2)/d(x)+d(1)/d(x)+d(x(−1))/d(x)

4. Calculate the derivative of each term.

2*x+0−1*x(−2)

5. Simplify the result by rewriting the negative exponent as a fraction.

2*x−1/(x2)

Final Answer

d()/d(x)(x3+x+1)/x=2*x−1/(x2)

Want more problems? Check here!