Find the derivative of y=e^(2x)*(x^2-4x-2).
Notice that y can be expressed as y=f(x)g(x), in which f(x)=e^(2x) and g(x)=x^2-4x-2.Through the product rule, we know that dy/dx=f'(x)g(x)+f(x)g'(x).Through the chain rule, we can solve f(x) by rewriting in the form f=e^u, u=2xf'(x)=df/du * du/dxf('x)=e^u * 2f'(x)=2e^(2x)We solve g(x) by simply differentiating a polynomial function with degree 2, i.e. given the term ax^b we replace it with abx^(b-1)g'(x)=2x-4Therefore, dy/dx = 2e^(2x)(x^2-4x-2) + e^(2x)*(2x-4).
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