What is the derivative of $y=3x^2e^(5x)$ ?

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Answer 1 · 2014-07-24T02:17:02

This is a product of the function $3x^2$ and the function $e^(5x)$ , which is itself the composite of the functions given by $e^x$ and by $5x$ .

Thus we will need the product rule to the effect that:

$(3x^2 e^(5x))'=(3x^2)'e^(5x)+3x^2(e^(5x))'$

As well as the fact that:

$(3x^2)'=6x$

Using these basic differentiation rules, and the Chain Rule combined with $(e^x)'=e^x$ , we can calculate that:

$(e^(5x))'=e^(5x)\times (5x)'=5e^(5x)$ .

As a result:

$(3x^2 e^(5x))'=6xe^(5x)+15x^2e^(5x)$ .

What is the derivative of y=3x^2e^(5x)y=3x^2e^(5x) ?