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Step-by-step Solution

Find the derivative (d/dx)(e^(2x)-x*cos(x*y)) using the sum rule

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Answer

$2e^{2x}-\left(\cos\left(xy\right)-xy\sin\left(xy\right)\right)$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(e^{2x}-x\cdot \cos\left(xy\right)\right)$
1

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(e^{2x}\right)+\frac{d}{dx}\left(-x\cos\left(xy\right)\right)$
2

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$\frac{d}{dx}\left(e^{2x}\right)-\frac{d}{dx}\left(x\cos\left(xy\right)\right)$

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Answer

$2e^{2x}-\left(\cos\left(xy\right)-xy\sin\left(xy\right)\right)$
$\frac{d}{dx}\left(e^{2x}-x\cdot \cos\left(xy\right)\right)$

Main topic:

Product rule

Used formulas:

5. See formulas

Time to solve it:

~ 4.36 seconds