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Given that $y = ext{ln}(5x)$ find \( \frac{dy}{dx} \) Circle your answer. - AQA - A-Level Maths Pure - Question 2 - 2021 - Paper 1
Question 2
Given that $y = ext{ln}(5x)$ find \( \frac{dy}{dx} \) Circle your answer.
Worked Solution & Example Answer:Given that $y = ext{ln}(5x)$ find \( \frac{dy}{dx} \) Circle your answer. - AQA - A-Level Maths Pure - Question 2 - 2021 - Paper 1
Step 1
find \( \frac{dy}{dx} \)
Answer
To find ( \frac{dy}{dx} ) of the function ( y = ext{ln}(5x) ), we will use the chain rule of differentiation. The chain rule states that if ( y = ext{ln}(u) ), then ( \frac{dy}{dx} = \frac{1}{u} \cdot \frac{du}{dx} ).
In this case, ( u = 5x ). Thus,
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First, differentiate ( u ) with respect to ( x ): [ \frac{du}{dx} = 5. ]
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Now, apply the chain rule: [ \frac{dy}{dx} = \frac{1}{5x} \cdot 5 = \frac{1}{x}. ]
So, the final answer is: [ \frac{dy}{dx} = \frac{1}{x}. ]