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extra coeff's added

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This question takes ideas from all previous parts of the 'Differentiation' series. If you struggle, look back at the appropriate sections.

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$f(x)=\\var{ex[0]}e^x\\sin(\\var{c[0]}x)$

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$f'(x)=$ [[0]]

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$f(x)=\\var{ex[1]}\\sin(\\var{c[1]}x)\\cos(\\var{c[2]}x)$

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$f'(x)=$ [[0]]

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$f(x)=$  $\\ln(\\var{ex[2]}x)$$\\var{c[3]}-\\var{c[4]}x$

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$f'(x)=$ [[0]]

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$f(x)=\\var{ex[3]}\\sin(\\ln(x))$

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$f'(x)=$ [[0]]

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$f(x)=$  $e^{\\var{p}x}$$\\var{c[5]}-x$

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$f'(x)=$ [[0]]

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$f(x)=\\ln(\\var{ex[4]}x)\\sin(\\var{ex[5]}x)$

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$f'(x)=$ [[0]]

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Find $f'(x)$ of the following, using the appropriate rule.

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Identifying the correct rule to use

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