Question

Differentiate the following w.r.t. x:
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Answer 1

${ \bold{ \boxed{ \boxed{ \mathfrak{ \huge\red{ \bigstar \: answer \: \bigstar}}}}}}$

${ \bold{ \underline{ Given \: \: function} : - }} \\ \\ { \bold { \orange{ \implies \: {e}^{x} + {e}^{ {x}^{2} } + {e}^{ {x}^{3} } + {e}^{ {x}^{4} } + {e}^{ {x}^{5} } }}}$

${ \bold { \underline{To \: \: find} : - }} \\ \\{ \bold{ \orange{ { DIFFERENTIATION }}}} \\ \\ { \bold{ \boxed{ \boxed{\green{ \mathtt{ \huge{ \bigstar \: solution \bigstar}}}}}}}$

${ \bold{ \orange{y = {e}^{x} + {e}^{ {x}^{2} } + {e}^{ {x}^{3} } + {e}^{ {x}^{4} } + {e}^{ {x}^{5} } }}} \\ \\ { \bold{ \orange{ \frac{dy}{dx} = {e}^{x} + {e}^{ {x}^{2} }(2x) + {e}^{ {x}^{ 3} } (3 {x}^{2} ) + {e}^{ {x}^{4} } (4 {x}^{3} ) + {e}^{ {x}^{5} } (5 {x}^{4} )}}} \\ \\ { \bold{ \orange{ \frac{dy}{dx} = {e}^{x} + 2x {e}^{ {x}^{2} } + 3 {x}^{2} {e}^{ {x}^{3} } + 4 {x}^{3} {e}^{ {x}^{4} } + 5 {x}^{4} {e}^{ {x}^{5} } }}}$

${ \bold{ \red{ \underline{used \: \: formula} : - } }} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: \: . \: \: \frac{d( {x}^{n} )}{dx} = n {x}^{n - 1} }}} \\ \\ { \bold{ \blue{ \: \: \: \: \: \: \: . \: \: \frac{d( {e}^{x}) }{dx} = {e}^{x} }}}$

${ \bold{ \red{ \boxed{ \huge{ \mathfrak{hope \: \: you \: \: like \: \: it...}}}}}}$