Year 12 Maths Advanced (2027) Differential calculus

Differentiating Exponentials & Logs with Other Bases

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Questions

Question 1

147084

Differentiate \(y = {2^x}\)

Answer

\( \ln 2 \times {2^x}\)

Worked Solution

\begin{aligned}
y &=2^{x} \\
\log _{2} y &=x \\
x &=\frac{\ln y}{\ln 2} \\
\frac{d x}{d y} &=\frac{1}{\ln 2} \times \frac{1}{y} \\
\frac{d y}{d x} &=\ln 2 \times y \\
&=\ln 2 \times 2^{x}
\end{aligned}

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