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4)
![{a}^{x} times ln(10) times (1 times tan(x) + x times frac{1}{ {( cos(x)) }^{2} } ) {a}^{x} times ln(10) times (1 times tan(x) + x times frac{1}{ {( cos(x)) }^{2} } )](https://tex.z-dn.net/?f=+%7Ba%7D%5E%7Bx%7D++times++ln%2810%29++times+%281+times++tan%28x%29++%2B+x+times+frac%7B1%7D%7B++%7B%28+cos%28x%29%29+%7D%5E%7B2%7D++%7D+%29)
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![= 2 sin(2x) times 2 times cos( frac{x}{2} ) + { (sin(2x)) }^{2} times ( - sin( frac{x}{2}) times frac{1}{2} ) = 2 sin(2x) times 2 times cos( frac{x}{2} ) + { (sin(2x)) }^{2} times ( - sin( frac{x}{2}) times frac{1}{2} )](https://tex.z-dn.net/?f=+%3D+2+sin%282x%29++times+2+times++cos%28+frac%7Bx%7D%7B2%7D+%29++%2B++%7B+%28sin%282x%29%29+%7D%5E%7B2%7D+times+%28+-++sin%28+frac%7Bx%7D%7B2%7D%29+times++frac%7B1%7D%7B2%7D++%29++)
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![frac{(2x times ln(x) + {x}^{2} times frac{1}{x} ) times (x - 2) - {x}^{2} times ln(x) times 1 }{(x - 2)^{2} } frac{(2x times ln(x) + {x}^{2} times frac{1}{x} ) times (x - 2) - {x}^{2} times ln(x) times 1 }{(x - 2)^{2} }](https://tex.z-dn.net/?f=+frac%7B%282x+times++ln%28x%29+%2B++%7Bx%7D%5E%7B2%7D+times++frac%7B1%7D%7Bx%7D+%29+times+%28x+-+2%29+-++%7Bx%7D%5E%7B2%7D+times++ln%28x%29++times+1+++%7D%7B%28x+-+2%29%5E%7B2%7D+%7D+)
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