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3 years ago

5

Connor went to the country fair with $22.50 in his pocket. He bought a hot dog and drink for $3.75 and then wanted to spend the

rest of his money on ride tickets, which cost $1.25 each right any quality to represent the total spent there are the number of tickets purchased

1 answer:

KatRina [158]3 years ago

3 0

22.50-3.75= 18.75
18.75/1.25= 15
1.25 × X = total money left after purchases.

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Step-by-step explanation:

we would like to figure out the differential coefficient of $e^{2x}(1+\ln(x))$

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$\displaystyle \frac{d}{dx} {e}^{2x}$

the rule of composite function derivation is given by:

$\rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dg} f(g(x)) \times \frac{d}{dx} g(x)$

so let g(x) [2x] be u and transform it:

$\displaystyle \frac{d}{du} {e}^{u} \cdot \frac{d}{dx} 2x$

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$\displaystyle {e}^{u} \cdot 2$

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$\displaystyle \boxed{2{e}^{2x} }$

Part-B: differentiating ln(x)•e^2x

Product rule of differentiating is given by:

$\displaystyle \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)$

let

$f(x) \implies \ln(x)$
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substitute

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differentiate:

$\rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \boxed{\frac{1}{x} {e}^{2x} + 2\ln(x) {e}^{2x} }$

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substitute what we got:

$\rm \displaystyle y' = \boxed{2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} }$

and we're done!

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