Question: "Find the derivative of the following functions y=10ln⁡2x"

College
Calculus and Analysis
Differential Calculus
Derivatives

Rivka Thorpe

Answered question

2021-10-21

Find the derivative of the following functions

y = 10^{\ln 2 x}

Answer & Explanation

sovienesY

Skilled2021-10-22Added 89 answers

Step 1
The chain rule is applied
$y = 10^{\ln (2 x)}$
$\frac{d y}{d x} = 10^{\ln (2 x)} \ln (10) \frac{d}{d x} \ln (2 x)$
Step 2
Again, we apply the chain rule
$\frac{d y}{d x} = 10^{\ln (2 x)} \ln (10) \frac{1}{2 x} \frac{d}{d x} (2 x)$

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

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

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

Result: $\frac{10^{\ln (2 x)} \ln (10)}{x}$

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