Question

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

Answer 1

Answer: e² - 4

Step-by-step explanation:

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

Answer 2

Answer:

$\dfrac{\text{d}y}{\text{d}x} = 2e^{2x}+12e^{-4x}$

Step-by-step explanation:

Given function:

$y=e^{2x}-3e^{-4x}$

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

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

Therefore:

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