Question

question find the differential dy of the function y = 3x^4+2x^2 + 1. provide your answer below: dy/dx=

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=nax^{n - 1}$. For the function $y = 3x^4+2x^2 + 1$, we differentiate each term separately.
For the term $3x^4$, using the power - rule: $\frac{d}{dx}(3x^4)=4\times3x^{4 - 1}=12x^3$.
For the term $2x^2$, using the power - rule: $\frac{d}{dx}(2x^2)=2\times2x^{2 - 1}=4x$.
For the constant term $1$, since the derivative of a constant $c$ is $0$ ($\frac{d}{dx}(c)=0$), $\frac{d}{dx}(1) = 0$.

Step2: Combine the derivatives of each term

$dy=(12x^3 + 4x+0)dx$. So, $\frac{dy}{dx}=12x^3 + 4x$.

Answer:

$12x^3 + 4x$