Use the rules for derivatives to find the derivative of

Pearl Carney

Pearl Carney

Answered question

2021-12-03

Use the rules for derivatives to find the derivative of function defined as follows.
y=ln|2x1|x+3

Answer & Explanation

Opeance1951

Opeance1951

Beginner2021-12-04Added 26 answers

Step 1
The given function is:
y=ln|2x1|x+3
To find the derivative of this function, apply the quotient rule,
ddx(uv)=vddx(u)uddx(v)v2
Step 2
So,
dydx=ddx(ln|2x1|x+3)
dydx=(x+3)ddx(ln|2x1|)(ln|2x1|)ddx(x+3)(x+3)2
dydx=(x+3)×2(2x1)(ln|2x1|)(x+3)2
dydx=2(x+3)(2x1)(ln|2x1|)(x+3)2
dydx=2(x+3)(2x1)(ln|2x1|)(x+3)2

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