If y=(3 x²+1)(x³+2 x) then \;d y/d x is

Correct Answer is : 15x4+21x2+215 x^{4}+21 x²+215x4+21x2+2

Correct Answer is : 15x4+21x2+215 x^{4}+21 x²+215x4+21x2+2

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Differential Calculus

Question : 41 of 69

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y=(3 x^{2}+1)(x^{3}+2 x)

\;\frac{d y}{d x}

Solution:

Concept:

Use the product rule for differentiation:

\frac{d}{dx}(uv) = u'v + uv'

Explanation:

Let

u = 3x^2 + 1

and

v = x^3 + 2x

Then

u' = 6x

and

v' = 3x^2 + 2

Now

\frac{dy}{dx} = u'v + uv' = (6x)(x^3+2x) + (3x^2+1)(3x^2+2)

Simplify:

6x^4 + 12x^2 + (9x^4 + 6x^2 + 3x^2 + 2) = 6x^4 + 12x^2 + 9x^4 + 9x^2 + 2

Combine like terms:

15x^4 + 21x^2 + 2

Answer:

15x^{4}+21x^{2}+2

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