Step-by-step Solution

Find the derivative $\frac{d}{dx}\left(e^{2x}-x\cos\left(xy\right)\right)$ using the sum rule

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Step-by-step explanation

Problem to solve:

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

Learn how to solve sum rule of differentiation problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(e^(2x)-x*cos(x*y)) using the sum rule. The derivative of a sum of two functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\cos\left(xy\right). Solve the product -(\frac{d}{dx}\left(x\right)\cos\left(xy\right)+x\frac{d}{dx}\left(\cos\left(xy\right)\right)).

Final Answer

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

Related formulas:

5. See formulas

Time to solve it:

~ 0.04 s (SnapXam)