Mathematics

Problem

A student attempts to write the third derivative of

y

with respect to

x

as follows: Step 1:

y'=\dfrac{dy}{dx}

Step 2:

y''=\dfrac{d^{2}y}{dx^{2}}

Step 3:

y'''=\dfrac{d^{3}y}{dx^{2}}

Which statement correctly evaluates the notation used in Step 3? a) Step 3 is correct because a third derivative has a power of 3 only in the numerator. b) Step 3 is incorrect because the power on

dx

should also be 3. c) Step 3 is incorrect because it should be written as

\dfrac{d^{3}y}{d^{3}x}

. d) Step 3 is incorrect because it should be written as

\dfrac{dy^{3}}{dx^{3}}

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