Question

If y = (x²+1)(x³+3) then dy/dx is

Answer 1

Answer:

5x⁴ + 3x² + 6x

Step-by-step explanation:

Using the product rule:

$\frac{dy}{dx} = \frac{d}{dx}(x^2+1)\times(x^3+3)+(x^2+1)\times\frac{d}{dx}(x^3+3)\\\\= 2x\times(x^3+3) + (x^2+1)\times 3x^2\\\\= 2x(x^3+3)+3x^2(x^2+1)\\\\= 2x^4+6x+3x^4+3x^2\\\\= 5x^4+3x^2+6x$

Alternatively, expand first:

y = x⁵ + x³ + 3x² + 3

dy/dx = 5x⁴ + 3x² + 6x

Hope this helps and one of these approaches is what you needed.

Answer 2

Step-by-step explanation:

Using the product rule:

\begin{lgathered}\frac{dy}{dx} = \frac{d}{dx}(x^2+1)\times(x^3+3)+(x^2+1)\times\frac{d}{dx}(x^3+3)\\\\= 2x\times(x^3+3) + (x^2+1)\times 3x^2\\\\= 2x(x^3+3)+3x^2(x^2+1)\\\\= 2x^4+6x+3x^4+3x^2\\\\= 5x^4+3x^2+6x\end{lgathered}dxdy=dxd(x2+1)×(x3+3)+(x2+1)×dxd(x3+3)=2x×(x3+3)+(x2+1)×3x2=2x(x3+3)+3x2(x2+1)=2x4+6x+3x4+3x2=5x4+3x2+6x

Alternatively, expand first:

y = x⁵ + x³ + 3x² + 3

dy/dx = 5x⁴ + 3x² + 6x

it may help you

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