differentiate f(x)=(3x^2-5x)e^x

Question

Please help me

Answer 1

You can do this two ways:

 

1. Use Product Rule and Chain Rule. Split into two functions: f(x) = 3x²-5x, g(x) = e^x.

 

Derivative of f(x)g(x) = f'(x)g(x) + f(x)g'(x).

 

If f(x) = 3x²-5x, then f'(x) = 6x-5. If g(x) = e^x, then g'(x) = e^x.

 

Putting it together, the derivative of f(x)g(x) = (6x-5)(e^x) + (3x²-5x)(e^x). 

                                                                = e^x(6x-5+3x²-5x)

                                                                = e^x(3x²+x-5)

 

2. Distribute e^x to (3x²-5x) to get 3x²e^x - 5xe^x. Then use the Chain Rule. Answer should be the same as in 1. above.