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The differentiation sequence to remember is as follows.

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\$\\sin(x)\\rightarrow\\cos(x)\\rightarrow-\\sin(x)\\rightarrow-\\cos(x)\$

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If you would like to understand the proof, it can be found here.

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The derivative of $\\tan(x)$ is $\\sec^2(x)$.

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The proof is here.

Differentiation of trigonometric functions

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$y=\\var{c[0]}\\sin(x)$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\var{d[0]}\\cos(x)$

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$\\frac{dy}{dx}=$ [[0]]

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$y=-\\sin(x)+\\var{d[2]}x^2$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\var{d[1]}\\sin(x)-\\var{c[1]}\\cos(x)$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\var{c[2]}\\tan(x)$

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$\\frac{dy}{dx}=$ [[0]]

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Differentiate the following trigonometric functions.

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Do not write out $dy/dx$; only input the differentiated right hand side of each equation.

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Remember to bracket the argument of the trigonometric functions, for example, write $\\sin$$x$ as $\\sin(x)$.

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