Find the Derivative - d/dx (x/3.6+3.6/x)(x^2+1)

Problem

d()/d(x)*(x/3.6+3.6/x)*(x2+1)

Solution

1. Expand the expression by multiplying the two binomials to make differentiation easier.

(x/3.6+3.6/x)*(x2+1)=(x3)/3.6+x/3.6+3.6*x+3.6/x

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

1/3.6*x3+1/3.6*x+3.6*x+3.6*x(−1)

3. Combine the like terms involving x

1/3.6≈0.2777...

1/3.6*x+3.6*x=(1/3.6+3.6)*x

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

d()/d(x)(x3)/3.6=(3*x2)/3.6

d()/d(x)*(1/3.6+3.6)*x=1/3.6+3.6

d()/d(x)*3.6*x(−1)=−3.6*x(−2)

5. Simplify the coefficients and combine the results.

3/3.6=1/1.2=5/6

1/3.6+3.6=10/36+36/10=5/18+18/5=(25+324)/90=349/90

Final Answer

d()/d(x)*(x/3.6+3.6/x)*(x2+1)=(5*x2)/6+349/90−3.6/(x2)

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