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Let y = e³ˣsin x. Find y' and y'' at x = 0.

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Let $y = e^{3x}\sin x$ . Find $y'$ and $y''$ at $x = 0$ .

Need a reminder? The key ideaShow

$f''$ is the derivative of $f'$ , and $f^{(n)}$ is the $n$ th derivative. For a parametric curve, $\dfrac{d^2y}{dx^2} = \dfrac{d}{dt}\left(\dfrac{dy}{dx}\right)\Big/\dfrac{dx}{dt}$ . To verify a relation, differentiate twice and substitute.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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Let y = e³ˣsin x. Find y' and y'' at x = 0.

The worked solution

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