Question

If y = 3x^2.e^x, differentiate with respect to x.

3x^2e^x(x+3)
3x^2e^x(x-3)
3x(x+3)
3x^2

Answer 1

Answer on Question #47037 – Math – Differential Calculus | Equations

Question:

If $y = 3x^2.e^x$, differentiate with respect to $x$.

$$3x^2e^x(x+3)$$ $$3x^2e^x(x-3)$$ $$3x(x+3)$$ $$3x^2$$

Solution:

The product rule: For the functions $f$ and $g$, the derivative of the function $h(x) = f(x)g(x)$ with respect to $x$ is the following:

$$h'(x) = f(x)g'(x) + f'(x)g(x)$$

Therefore:

$$y' = 3x^2(e^x)' + (3x^2)'e^x = 3x^2e^x + 3 \cdot 2x\,e^x = 3x\,e^x(x + 2)$$

Answer: $3x\,e^x(x + 2)$

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