Question

dy/dxif y = 4x3 + 3x2 + 2

Answer 1

The function is 

                                $\displaystyle{ y=4x^3+3x^2+2$.

We recall that the derivative of each monomial $ax^b$ is $a\cdot b\cdot x^{b-1}$, and the derivative of a constant (function) is 0.

According to this:

$\frac{d}{dx}(4x^3+3x^2+2)=4\cdot 3\cdot x^2 + 3\cdot 2\cdot x+0 =12x^2+6x$.


Answer: $12x^2+6x$

Answer 2

Answer:

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will use the general rules for differentiation. Rest of the, procedure are given below -

So,

$= \frac{dy}{dx}$

$= \frac{d}{dx} ( {4x}^{3} + {3x}^{2} + 2)$

$= \frac{d}{dx} ( {4x}^{3}) + \frac{d}{dx} ( {3x}^{2} ) + \frac{d}{dx} (2)$

$= (4 \times 3 \times x {}^{(3 - 1)} + (3 \times 2 \times x {}^{(2 - 1)} + 0$

$= 12 {x}^{2} + 6x$

(This will be considered as the final answer of the given differentiation. d/dx of 2 is equal to zero, because 2 is a constant here.)

Hence, the answer will be 12x²+6x