What is the derivative of the following f(x) = e^x*sin(2x^2 - 4x)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The derivative of the function f(x) = e^x*sin(2x^2 - 4x) has to be determined.

Use the product rule, that gives the derivative of f(x) = g(x)*h(x) as f'(x) = g'(x)*h(x) + g(x)*h'(x)

For f(x) = e^x*sin(2x^2 - 4x)

f'(x) = (e^x)'*sin(2x^2 - 4x) + e^x*(sin(2x^2 - 4x))'

= e^x*sin(2x^2 - 4x) + e^x*(sin(2x^2 - 4x))'

Use the chain rule; for f(x) = g(h(x)), f'(x) = g'(h(x))*h'(x)

= e^x*sin(2x^2 - 4x) + e^x*cos(2x^2 - 4x)*(4x - 4)

The derivative of f(x) = e^x*sin(2x^2 - 4x) is f'(x) = e^x*sin(2x^2 - 4x) + e^x*cos(2x^2 - 4x)*(4x - 4)

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