Higher-Order Derivative of a Product

Question

Let $$g$$ be the function defined by $$g(x) = e^{2x}\cos(3x)$$. Which of the following is an expression for $$\frac{d^3g}{dx^3}$$?

Accepted Answer

$$-46e^{2x}\cos(3x) - 9e^{2x}\sin(3x)$$

Answer

$$-8e^{2x}\sin(3x) - 27e^{2x}\cos(3x)$$

Answer

$$8e^{2x}\cos(3x) - 36e^{2x}\cos(3x) - 36e^{2x}\sin(3x)$$

Answer

$$8e^{2x}\cos(3x) - 36e^{2x}\sin(3x)$$

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