Find dy/dx y=1/(x+2)

Problem

d()/d(x)1/(x+2)

Solution

1. Identify the function as a reciprocal or a power function by rewriting it with a negative exponent.

y=(x+2)(−1)

2. Apply the power rule and the chain rule, where the derivative of un is n*u(n−1)⋅d(u)/d(x)

d(y)/d(x)=−1*(x+2)(−2)⋅d(x+2)/d(x)

3. Differentiate the inner function x+2 with respect to x

d(x+2)/d(x)=1

4. Simplify the expression by multiplying the terms and moving the negative exponent back to the denominator.

d(y)/d(x)=−1/((x+2)2)

Final Answer

d()/d(x)1/(x+2)=−1/((x+2)2)

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