Find the Derivative - d/dx (x/3.1+3.1/x)(x^2+1)

Problem

d()/d(x)*(x/3.1+3.1/x)*(x2+1)

Solution

1. Expand the expression by multiplying the two binomials to simplify the differentiation process.

(x/3.1+3.1/x)*(x2+1)=(x3)/3.1+x/3.1+3.1*x+3.1/x

2. Rewrite the terms using power notation to prepare for the power rule.

1/3.1*x3+1/3.1*x+3.1*x+3.1*x(−1)

3. Combine like terms involving x to reduce the number of operations.

1/3.1*x3+(1/3.1+3.1)*x+3.1*x(−1)

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

d()/d(x)*(1/3.1*x3+(1/3.1+3.1)*x+3.1*x(−1))=(3*x2)/3.1+(1/3.1+3.1)−3.1*x(−2)

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

(3*x2)/3.1+1/3.1+3.1−3.1/(x2)

Final Answer

d()/d(x)*(x/3.1+3.1/x)*(x2+1)=(3*x2+1)/3.1+3.1−3.1/(x2)

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