Respuesta :
The function is
[tex]\displaystyle{ y=4x^3+3x^2+2[/tex].
We recall that the derivative of each monomial [tex]ax^b[/tex] is [tex]a\cdot b\cdot x^{b-1}[/tex], and the derivative of a constant (function) is 0.
According to this:
[tex] \frac{d}{dx}(4x^3+3x^2+2)=4\cdot 3\cdot x^2 + 3\cdot 2\cdot x+0 =12x^2+6x[/tex].
Answer: [tex]12x^2+6x[/tex]
[tex]\displaystyle{ y=4x^3+3x^2+2[/tex].
We recall that the derivative of each monomial [tex]ax^b[/tex] is [tex]a\cdot b\cdot x^{b-1}[/tex], and the derivative of a constant (function) is 0.
According to this:
[tex] \frac{d}{dx}(4x^3+3x^2+2)=4\cdot 3\cdot x^2 + 3\cdot 2\cdot x+0 =12x^2+6x[/tex].
Answer: [tex]12x^2+6x[/tex]
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,
[tex] = \frac{dy}{dx} [/tex]
[tex] = \frac{d}{dx} ( {4x}^{3} + {3x}^{2} + 2)[/tex]
[tex] = \frac{d}{dx} ( {4x}^{3}) + \frac{d}{dx} ( {3x}^{2} ) + \frac{d}{dx} (2)[/tex]
[tex] = (4 \times 3 \times x {}^{(3 - 1)} + (3 \times 2 \times x {}^{(2 - 1)} + 0[/tex]
[tex] = 12 {x}^{2} + 6x[/tex]
(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
