Calculus Help Show that one function is not an antiderivative of another
1 answer:
Just differentiate <em>G</em> and <em>H</em> :
• d<em>G</em>/d<em>x</em> = d(<em>x</em> ² <em>eˣ </em>)/d<em>x</em> = 2<em>x</em> <em>eˣ</em> + <em>x</em> ² <em>eˣ</em>
so <em>G</em> is not an antiderivative of <em>f</em>.
• d<em>H</em>/d<em>x</em> = d(2<em>x</em> <em>eˣ</em> - 2<em>eˣ</em> ) = (2<em>eˣ</em> + 2<em>x</em> <em>eˣ</em> ) - 2<em>eˣ</em> = 2<em>x</em> <em>eˣ</em> = <em>f(x)</em>
so <em>H</em> is indeed an antiderivative of <em>f</em>.
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