How do you differentiate $y = {(6 x^{2} + 2 x)}^{3}$ $y=(6x^2 + 2x)^3$ ?

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How do you differentiate $y = {(6 x^{2} + 2 x)}^{3}$ $y=(6x^2 + 2x)^3$ ?

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Answer 1 · 2018-03-07T02:16:55

$\frac{d y}{d x} = 3 (12 x + 2) {(6 x^{2} + 2 x)}^{2}$ $dy/dx= 3(12x + 2)(6x^2 + 2x)^2$

Explanation:

Don't bother expanding, just use the chain rule. Let $u = 6 x^{2} + 2 x$ $u = 6x^2+2x$ . Then $d u = 12 x + 2$ $du = 12x + 2$ . This also means that $y = u^{3}$ $y = u^3$ ., or $y = 3 u^{2}$ $y = 3u^2$ .

$\frac{d y}{d x} = (12 x + 2) 3 {(6 x^{2} + 2 x)}^{2}$ $dy/dx = (12x +2)3(6x^2 + 2x)^2$

$\frac{d y}{d x} = 3 (12 x + 2) {(6 x^{2} + 2 x)}^{2}$ $dy/dx= 3(12x + 2)(6x^2 + 2x)^2$

Hopefully this helps!

Answer 2 · 2018-03-07T02:21:20

$3 {(6 x^{2} + 2 x)}^{2} (12 x + 2)$ $3(6x^2+2x)^2(12x+2)$

Explanation:

Applying the chain rule we arrive at the consensus that $d/dx f(g(x)) = f'(g(x))*g'(x)$
we identify the variables within our problem and define that $f(x) = x^3$ and
$f'(x)=3(x)^2$
$g(x) = 6x^2+2x$
combining the functions together with recieve the original function
$g'(x)=12x+2$ using the power rule $Px^(P-1)$
from this point we plug out g(x) and f(x) functions into our rules of derivatives.

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How do you differentiate $y = {(6 x^{2} + 2 x)}^{3}$ $y=(6x^2 + 2x)^3$ ?

2 Answers

Explanation:

Explanation:

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Science

Math

Humanities

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How do you differentiate y=(6x^2 + 2x)^3y=(6x2+2x)3y=(6x^2 + 2x)^3?

2 Answers

Explanation:

Explanation:

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How do you differentiate $y = {(6 x^{2} + 2 x)}^{3}$ $y=(6x^2 + 2x)^3$ ?