Question

question find the differential dy of the function y = 3x^6+4x^3 + 3x^2 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 $y = 3x^6+4x^3 + 3x^2$, we differentiate each term separately.
For the first term $y_1 = 3x^6$, $\frac{dy_1}{dx}=6\times3x^{6 - 1}=18x^5$.
For the second term $y_2 = 4x^3$, $\frac{dy_2}{dx}=3\times4x^{3 - 1}=12x^2$.
For the third term $y_3 = 3x^2$, $\frac{dy_3}{dx}=2\times3x^{2 - 1}=6x$.

Step2: Sum up the derivatives of each term

Since $y=y_1 + y_2+y_3$, then $\frac{dy}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}+\frac{dy_3}{dx}$.
$\frac{dy}{dx}=18x^5+12x^2 + 6x$.

Answer:

$18x^5+12x^2 + 6x$