Question

Differentiate x2 +3x+1 w.r.t x​

Answer 1

Answer:

$x^{2} +3x+1$

=$d(x^{2} +3x+1)/dx$

=$d(x^2)/dx+d(3x)/dx+0$

=$2x+3$

Step-by-step explanation:

Answer 2

Differentiation

The following are the tips and concepts that can be used to find the solution:

Power rule: It is used to differentiate expressions like $x^n$. The power rule is:

$\longrightarrow \dfrac{d}{dx}(x^n) = nx^{n-1}$

Constant rule: It is used to differentiate expressions like $c$, where $c$ is a constant. The constant rule is:

$\longrightarrow \dfrac{d}{dx}(c) = 0$

We have been asked to differentiate the following expression with respect to $x$:

$\longrightarrow x^2 + 3x + 1$

Solution:

By the Sum Rule, the derivative of $x^2 + 3x + 1$ with respect to $x$ is:

$\implies \dfrac{d}{dx} (x^2) + \dfrac{d}{dx}(3x) + \dfrac{d}{dx}(1)$

$\implies 2x^{2-1} + 3\dfrac{d}{dx}(x) + \dfrac{d}{dx}(1)$

$\implies 2x + 3(1) + 0$

$\implies \boxed{2x + 3}$

Hence, this is the answer.