Question
Differentiate the following function with respect to x:
$\text{x}^3\text{e}^\text{x}\cos\text{x}$
$\text{x}^3\text{e}^\text{x}\cos\text{x}$
Then,
$\text{u}'=\text{3x}^2;\text{v}'=\text{e}^\text{x};\text{w}'=-\sin\text{x}$Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uvw})=\text{u}'\text{vw}+\text{uv}'\text{w}+\text{uv}\text{w}'$
$\frac{\text{d}}{\text{dx}}(\text{x}^3\text{e}^\text{x}\cos\text{x})=\text{3x}^2\text{e}^\text{x}\cos\text{x}+\text{x}^3\text{e}^\text{x}\cos\text{x}+\text{x}^3\text{e}^\text{x}(-\sin\text{x})$
$=\text{x}^2\text{e}^\text{x}(\text{3}\cos\text{x}+\text{x}\cos\text{x}-\text{x}\sin\text{x})$
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focus is (-2, 3), directrix is 2x + 3y + 4 = 0 and
$\text{e}=\frac{4}{5}.$Find the middle term in the expansion of:
$\Big(\frac{2}{3}\text{x}-\frac{3}{2\text{x}}\Big)^{20}$