Differentiation of Different Functions (VCE SSCE Mathematical Methods): Flashcards

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Differentiation of Different Functions
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Unique property of exe^x

It is its own derivative

Approx. value of Euler's number ee

eapprox2.71828e approx 2.71828

Derivative of exe^x

exe^x

Derivative of ekxe^{kx} (k constant)

kekxke^{kx}

Derivative of ef(x)e^{f(x)} (chain rule)

f(x)ef(x)f'(x)e^{f(x)}

Derivative of loge(kx)\log_e(kx) where k>0k > 0

1x\frac{1}{x}

Derivative of loge(ax+b)\log_e(ax + b)

aax+b\frac{a}{ax + b}

Derivative of loge(f(x))\log_e(f(x)) (chain rule)

f(x)f(x)\frac{f'(x)}{f(x)}

Notation for natural logarithm

loge(x)\log_e(x) or ln(x)\ln(x)

Natural log relation to exe^x

Inverse of exe^x

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