Find the Derivative - d/dx (x/3.3+3.3/x)(x^2+1)

Problem

d()/d(x)*(x/3.3+3.3/x)*(x2+1)

Solution

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

(x/3.3+3.3/x)*(x2+1)=(x3)/3.3+x/3.3+3.3*x+3.3/x

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

1/3.3*x3+1/3.3*x+3.3*x+3.3*x(−1)

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

1/3.3*x3+(1/3.3+3.3)*x+3.3*x(−1)

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

d()/d(x)*(1/3.3*x3+(1/3.3+3.3)*x+3.3*x(−1))=3/3.3*x2+(1/3.3+3.3)−3.3*x(−2)

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

1/1.1*x2+(1+3.3)/3.3−3.3/(x2)

6. Calculate the numerical values for the constant term.

(1+10.89)/3.3=11.89/3.3≈3.60303

Final Answer

d()/d(x)*(x/3.3+3.3/x)*(x2+1)=(x2)/1.1+11.89/3.3−3.3/(x2)

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