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The key fact to understand here is that the differentiate of $e^x$ is $e^x$.

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This can be proven by looking at evaluating limits etc. but it is not necessary to do so at this stage.

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The basic steps to differentiate an exponential function are:

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Differentiate the power of $e$, for example in Part b, $y=\\var{c[1]}e^{\\var{p[1]}x}$, you would differentiate $\\var{p[1]}x$.

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In this example, it is $\\var{p[1]}$.

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Then multiply the coefficient of $e$ by this result.

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Here, you would find $\\simplify{{c[1]}{p[1]}e^({p[1]}x)}$.

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Remember, don't be confused if there is no coefficient. The fact the term is there means the coefficient must be $1$, but we don't tend to write it out as, for example $1x$, we just say $x$.

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$y=e^x+\\var{c[4]}x^2+\\var{c[5]}x+\\var{c[6]}$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\var{c[1]}e^{\\var{p[1]}x}$

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$\\frac{dy}{dx}=$ [[0]]

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$y=\\var{c[2]}e^{\\var{p[2]}x}+\\sin(x)$

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$\\frac{dy}{dx}=$ [[0]]

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$y=-\\var{c[4]}\\tan(x)+\\var{c[3]}e^{\\var{p[3]}x}-\\cos(x)$

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$\\frac{dy}{dx}=$ [[0]]

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Differentiate the following.

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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 enclose all single powers inside a bracket, for example, $e^{2x}$ is inputted as $e$^$(2x)$.

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Differentiating exponentials

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