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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{dx}\left(e^{3x}\cos\left(4x\right)\right)+\frac{d}{dx}\left(-e^{-3x}\sin\left(2x\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(e^(3x)cos(4x)-e^(-3x)sin(2x)) using the sum rule. The derivative of a sum of two or more 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=e^{3x} and g=\cos\left(4x\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{-3x} and g=\sin\left(2x\right).