AM-1855

Differentiating standard functions

A Math · Secondary 4 · Medium · Differentiating standard functions

The equation of a curve is

y = 5e^{3x} - 2e^{-x}

.
Find

\dfrac{dy}{dx}

and state whether

y

is always increasing, always decreasing, or neither.

$\dfrac{dy}{dx} = 15e^{3x} + 2e^{-x}$ ; $y$ is always increasing
$\dfrac{dy}{dx} = 15e^{3x} - 2e^{-x}$ ; $y$ is always increasing
$\dfrac{dy}{dx} = 15e^{3x} + 2e^{-x}$ ; $y$ is always decreasing
$\dfrac{dy}{dx} = 5e^{3x} + 2e^{-x}$ ; $y$ is neither always increasing nor always decreasing

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