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Formula
Calculate the differentiation
Answer
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$\dfrac{d}{dx}{ \left(25x ^{ 2 } +30x+3 \right) }$
$50 x + 30$
Calculate the differentiation
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 30 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right)}$
$ $ It is $ \frac{d^{n}}{dx^{n}}{(f_1(x) + f_2(x) + ... + f_k(x))} = \frac{d^{n}}{dx^{n}}{f_1(x)} + \frac{d^{n}}{dx^{n}}{f_2(x)} + ... + \frac{d^{n}}{dx^{n}}{f_k(x)}$
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \right)} \color{#FF6800}{ + } \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 30 } \color{#FF6800}{ x } \right)} \color{#FF6800}{ + } \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 3 } \right)}$
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 25 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \right)} + \dfrac {d } {d x } {\left( 30 x \right)} + \dfrac {d } {d x } {\left( 3 \right)}$
$ $ It is $ \frac{d}{dx}{(c f(x))} = c \frac{d}{dx}{f(x)}$
$\color{#FF6800}{ 25 } \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \right)} + \dfrac {d } {d x } {\left( 30 x \right)} + \dfrac {d } {d x } {\left( 3 \right)}$
$25 \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \right)} + \dfrac {d } {d x } {\left( 30 x \right)} + \dfrac {d } {d x } {\left( 3 \right)}$
$ $ It is $ \frac{d}{dx}(x^{n}) = n x^{n-1}$
$25 \times \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } + \dfrac {d } {d x } {\left( 30 x \right)} + \dfrac {d } {d x } {\left( 3 \right)}$
$25 \times 2 x ^ { 2 - 1 } + \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 30 } \color{#FF6800}{ x } \right)} + \dfrac {d } {d x } {\left( 3 \right)}$
$ $ It is $ \frac{d}{dx}{(c f(x))} = c \frac{d}{dx}{f(x)}$
$25 \times 2 x ^ { 2 - 1 } + \color{#FF6800}{ 30 } \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } \right)} + \dfrac {d } {d x } {\left( 3 \right)}$
$25 \times 2 x ^ { 2 - 1 } + 30 \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ x } \right)} + \dfrac {d } {d x } {\left( 3 \right)}$
$ $ It is $ \frac{d}{dx}x = 1$
$25 \times 2 x ^ { 2 - 1 } + 30 \times \color{#FF6800}{ 1 } + \dfrac {d } {d x } {\left( 3 \right)}$
$25 \times 2 x ^ { 2 - 1 } + 30 \times 1 + \dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ 3 } \right)}$
$ $ If $ c $ is a constant, then it is $ \frac{d}{dx}c = 0$
$25 \times 2 x ^ { 2 - 1 } + 30 \times 1 + \color{#FF6800}{ 0 }$
$25 \times 2 x ^ { 2 - 1 } + 30 \times 1 \color{#FF6800}{ + } \color{#FF6800}{ 0 }$
$ $ 0 does not change when you add or subtract $ $
$25 \times 2 x ^ { 2 - 1 } + 30 \times 1$
$25 \times 2 x ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } } + 30 \times 1$
$ $ Subtract $ 1 $ from $ 2$
$25 \times 2 x ^ { \color{#FF6800}{ 1 } } + 30 \times 1$
$\color{#FF6800}{ 25 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ + } \color{#FF6800}{ 30 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 50 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 30 }$
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