Compute the derivative of the following function f(x)=\log_{5}(2x+1)

melodykap

melodykap

Answered question

2021-10-19

Compute the derivative of the following function
f(x)=log5(2x+1)

Answer & Explanation

Roosevelt Houghton

Roosevelt Houghton

Skilled2021-10-20Added 106 answers

We use the change of base property of log. Then we use the chain rule of the derivative.
f(x)=log5(2x+1)
f(x)=ln(2x+1)ln(5)
f(x)=ddxln(2x+1)ln(5)
f(x)=1ln(5)ddxln(2x+1)
f(x)=1ln(5)1(2x+1)ddx(2x+1)
f(x)=1ln(5)1(2x+1)(2)
f(x)=2ln(5)(2x+1)
Answer: f(x)=2ln(5)(2x+1)

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