Given that $y = x^4 + x^3 + 3$, find $\frac{dy}{dx}$. - Edexcel - A-Level Maths Pure - Question 3 - 2010 - Paper 2

To find $\frac{dy}{dx}$, we differentiate each term of the function $y = x^4 + x^3 + 3$ with respect to $x$:

$\frac{dy}{dx} = \frac{d}{dx}(x^4) + \frac{d}{dx}(x^3) + \frac{d}{dx}(3).$

Calculating the derivatives:

• The derivative of $x^4$ is $4x^3$.
• The derivative of $x^3$ is $3x^2$.
• The derivative of the constant $3$ is $0$.

Thus, we have:

$\frac{dy}{dx} = 4x^3 + 3x^2 + 0 = 4x^3 + 3x^2.$