Find the Derivative - d/dx y=x/6-6/x

Problem

d()/d(x)*(x/6−6/x)

Solution

1. Rewrite the expression using exponents to make differentiation easier.

x/6−6/x=1/6*x−6*x(−1)

2. Apply the sum rule for derivatives to differentiate each term independently.

d()/d(x)*(1/6*x−6*x(−1))=(d(1/6)*x)/d(x)−(d(6)*x(−1))/d(x)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to both terms.

(d(1/6)*x)/d(x)=1/6

(d(6)*x(−1))/d(x)=6*(−1)*x(−2)=−6*x(−2)

4. Combine the results and simplify the signs.

1/6−(−6*x(−2))=1/6+6*x(−2)

5. Convert the negative exponent back into a fraction.

1/6+6/(x2)

Final Answer

d()/d(x)*(x/6−6/x)=1/6+6/(x2)

Want more problems? Check here!