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Calculate the differentiation
Answer
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$2 ^ { 2 x + 1 } \ln { \left( 2 \right) }$
Calculate the differentiation
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ x } } \right)}$
$ $ If $ n $ is a positive number, it is $ \frac{d}{dx}{n^{f(x)}} = n^{f(x)} \ln(n) \frac{d}{dx}{f( x)}$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ x } } \ln { \left( \color{#FF6800}{ 2 } \right) } \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right)}$
$2 ^ { 2 x } \ln { \left( 2 \right) } \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right)}$
$ $ It is $ \frac{d}{dx}{(c f(x))} = c \frac{d}{dx}{f(x)}$
$2 ^ { 2 x } \ln { \left( 2 \right) } \times \color{#FF6800}{ 2 } \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } \right)}$
$2 ^ { 2 x } \ln { \left( 2 \right) } \times 2 \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } \right)}$
$ $ It is $ \frac{d}{dx}x = 1$
$2 ^ { 2 x } \ln { \left( 2 \right) } \times 2 \times \color{#FF6800}{ 1 }$
$2 ^ { 2 x } \ln { \left( 2 \right) } \times 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 }$
$ $ Multiplying any number by 1 does not change the value $ $
$2 ^ { 2 x } \ln { \left( 2 \right) } \times 2$
$2 ^ { 2 x } \times \color{#FF6800}{ 2 } \ln { \left( 2 \right) }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$2 ^ { 2 x } \times \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \ln { \left( 2 \right) }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ x } } \times \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \ln { \left( 2 \right) }$
$ $ Add the exponent as the base is the same $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \ln { \left( 2 \right) }$
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