Question

QUESTION 5
(a) Differentiate the following
(i)
y=e²x - 3e-4x

Answer 1

Answer: e² - 4

Explanation:

Differentiate of e²x - 3e-4x is e² - 4

Answer 2

`\frac{\text{d}y}{\text{d}x} = 2e^(2x)+12e^(-4x)`

Explanation:

Given function:

`y=e^(2x)-3e^(-4x)`

`\boxed{\begin{minipage}{3.7cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\frac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}`

`\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^(f(x))$}\\\\If $y=e^(f(x))$, then $\frac{\text{d}y}{\text{d}x}=f\:'(x)e^(f(x))$\\\end{minipage}}`

Therefore:

`\begin{aligned}\implies \frac{\text{d}y}{\text{d}x} & = \frac{\text{d}}{\text{d}x} e^(2x)-\frac{\text{d}}{\text{d}x}3e^(-4x)\\\\& =2 \cdot e^(2x)-(-4)\cdot 3 e^(-4x) \\\\ &= 2e^(2x)+12e^(-4x)\end{aligned}`