Find the derivative of the following functions \(\displaystyle{y}={10}^{{{\ln{{2}}}{x}}}\)

Samara Richard 2022-03-22 Answered

Find the derivative of the following functions

y = 10^{\ln 2 x}

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Regan Gallegos

Answered 2022-03-23 Author has 9 answers

Step 1
We use the chain rule

y = 10^{\ln (2 x)}

\frac{d y}{d x} = 10^{\ln (2 x)} \ln (10) \frac{d}{d x} \ln (2 x)

Step 2
We again use the chain rule

\frac{d y}{d x} = 10^{\ln (2 x)} \ln (10) \frac{1}{2 x} \frac{d}{d x} (2 x)

\frac{d y}{d x} = 10^{\ln (2 x)} \ln (10) \frac{1}{2 x} (2)

\frac{d y}{d x} = 10^{\ln (2 x)} \ln (10) \frac{1}{x}

\frac{d y}{d x} = \frac{10^{\ln (2 x)} \ln (10)}{x}

Answer:

\frac{10^{\ln (2 x)} \ln (10)}{x}

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