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Differentiate
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$y' = - \dfrac {\ln{\left( 2 \right)}} {2 ^ {x}}$
Differentiate
$\color{#FF6800}{y} = \color{#FF6800}{(\dfrac {1} {2}) ^ {x}}$
$ $ Find the derivative of this function $ $
$\color{#FF6800}{y'} = \color{#FF6800}{\dfrac{d}{dx}((\dfrac {1} {2}) ^ {x})}$
$y' = \dfrac{d}{dx}((\dfrac {1} {2}) ^ {x})$
$ $ To square the fraction, square the nominator and denominator individually $ $
$y' = \dfrac{d}{dx}(\dfrac {1} {2 ^ {x}})$
$y' = \color{#FF6800}{\dfrac{d}{dx}(\dfrac {1} {2 ^ {x}})}$
$ $ Solve it using $ \dfrac{d}{dx}(\dfrac {1} {f}) = - \dfrac {\dfrac{d}{dx}(f)} {f ^ {2}} $ differentiation $ $
$y' = \color{#FF6800}{- \dfrac {\dfrac{d}{dx}(2 ^ {x})} {(2 ^ {x}) ^ {2}}}$
$y' = - \dfrac {\dfrac{d}{dx}(2 ^ {x})} {(2 ^ {x}) ^ {2}}$
$ $ Organize it using $ \dfrac{d}{dx}(a ^ {x}) = \ln{\left( a \right)} \times a ^ {x} $ $ $
$y' = - \dfrac {\ln{\left( 2 \right)} \times 2 ^ {x}} {(2 ^ {x}) ^ {2}}$
$y' = - \dfrac {\ln{\left( 2 \right)} \times 2 ^ {x}} {(2 ^ {x}) ^ {2}}$
$ $ Solve the formula $ $
$y' = - \dfrac {\ln{\left( 2 \right)}} {2 ^ {\color{#FF6800}{x}}}$
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