Exponentials and Logarithms

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8 Terms

1
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Derivative of e to the x

y’ = e to the x

<p>y’ = e to the x</p>
2
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Derivative of complex exponential functions

y’ = f’(x) e to the power of f(x)

<p>y’ = f’(x) e to the power of f(x)</p>
3
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Applications of differentiation (exponentials base e)

To find stationary points, solve y’ = 0

To determine concavity, explore whether y’’ > 0 or y’’ < 0

To find points of inflexion y’’ = 0

To find tangents and normals to a curve

<p>To find stationary points, solve y’ = 0 </p><p>To determine concavity, explore whether y’’ &gt; 0 or y’’ &lt; 0 </p><p>To find points of inflexion y’’ = 0 </p><p>To find tangents and normals to a curve </p>
4
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Integration of Exponential Functions and applications of Integration (Standard)

Only works when the index is a linear function

<p>Only works when the index is a linear function</p>
5
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Integration of Exponential Functions and applications of Integration (Reference Sheet)

To remember, it is just the reverse of differentiating exponentials. You may need fudging.

<p>To remember, it is just the reverse of differentiating exponentials. You may need fudging. </p>
6
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Review of Logarithmic Functions

To remember, revise these rules.

<p>To remember, revise these rules.</p>
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Derivative of logarithm

Thus why if y = ln(x) y’ = 1/x

<p>Thus why if y = ln(x) y’ = 1/x</p>
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