Find the derivative of y - x 2-1 x 3-3- A- 5 x4-3 x2-xB- 4 x 4-3 x 2-6 xC- 5 x4-2 x2-6 xD- 5 x4-3 x2-6 x

The correct option is D 5x^4+3x^2+6xFrom the product rule with u=x^2+1 and v=x^3+3, we find ddx [(x^2+1)(x^3+3)] =(x^2+1)(3x^2 )+(x^3+3)(2x) =3x^4+3x^2+2x^4 ...

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Byju's Answer

Standard XII

Physics

Chain Rule of Differentiation

Find the deri...

Question

Find the derivative of $y = (x^{2} + 1) (x^{3} + 3)$ .

5 x^{4} + 3 x^{2} + x

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4 x^{4} + 3 x^{2} + 6 x

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5 x^{4} + 2 x^{2} + 6 x

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5 x^{4} + 3 x^{2} + 6 x

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Solution

The correct option is D $5 x^{4} + 3 x^{2} + 6 x$
From the product rule with $u = x^{2} + 1$ and $v = x^{3} + 3$ , we find
$\frac{d}{d x} [(x^{2} + 1) (x^{3} + 3)] = (x^{2} + 1) (3 x^{2}) + (x^{3} + 3) (2 x) = 3 x^{4} + 3 x^{2} + 2 x^{4} + 6 x \frac{d y}{d x} = 5 x^{4} + 3 x^{2} + 6 x$

Alternative:
$y = (x^{2} + 1) (x^{3} + 3) = x^{5} + x^{3} + 3 x^{2} + 3 \frac{d y}{d x} = 5 x^{4} + 3 x^{2} + 6 x$

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Find the derivative of y=(x2+1)(x3+3).

The correct option is D 5x4+3x2+6xFrom the product rule with u=x2+1 and v=x3+3, we find ddx[(x2+1)(x3+3)]=(x2+1)(3x2)+(x3+3)(2x)=3x4+3x2+2x4+6xdydx=5x4+3x2+6x Alternative: y=(x2+1)(x3+3)=x5+x3+3x2+3dydx=5x4+3x2+6x

Find the derivative of $y = (x^{2} + 1) (x^{3} + 3)$ .