Question

If y= 4x^3+3x^2+2 find dy/dx​

Answer 1

Answer:

By the Sum Rule, the derivative of

4

x

3

−

3

x

with respect to

x

is

d

d

x

[

4

x

3

]

+

d

d

x

[

−

3

x

]

.

d

d

x

[

4

x

3

]

+

d

d

x

[

−

3

x

]

Evaluate

d

d

x

[

4

x

3

]

.

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12

x

2

+

d

d

x

[

−

3

x

]

Evaluate

d

d

x

[

−

3

x

]

.

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12

x

2

−

3

Answer 2

given,

$y= 4x^3+3x^2+2\\=\frac{d}{dx}\left(4x^3+3x^2+2\right)\\\mathrm{Apply\:the\:Sum/Difference\:Rule}\\\quad \left(f\pm g\right)'=f\:'\pm g'\\=\frac{d}{dx}\left(4x^3\right)+\frac{d}{dx}\left(3x^2\right)+\frac{d}{dx}\left(2\right)\\\frac{d}{dx} (4x^3)\ =12x^2\\\\\frac{d}{dx}(3x^2)=6x \\\frac{d}{dx} (2)=0\\=12x^2+6x+0\\=12x^2+6x$