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Let y = log₁₀(x² + 1). Find dy/dx at x = 3, to four decimal places. Use ln 10 ≈ 2.302585.

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Let $y = \log_{10}(x^2 + 1)$ . Find $\dfrac{dy}{dx}$ at $x = 3$ , to four decimal places. Use $\ln 10 \approx 2.302585$ .

Need a reminder? The key ideaShow

$(e^x)' = e^x$ , $(a^x)' = a^x\ln a$ , $(\ln x)' = \dfrac{1}{x}$ , $(\log_a x)' = \dfrac{1}{x\ln a}$ , $(\sin^{-1}x)' = \dfrac{1}{\sqrt{1 - x^2}}$ , $(\tan^{-1}x)' = \dfrac{1}{1 + x^2}$ . Combine each with the chain rule.

The worked solution

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Let y = log₁₀(x² + 1). Find dy/dx at x = 3, to four decimal places. Use ln 10 ≈ 2.302585.

The worked solution

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