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Question

If y=(2x2+6x)(2x3+5x2), then dydx=

A
20x4+80x3+90x2
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B
20x4+88x3+90x2
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C
16x4+88x3+90x2
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D
16x4+80x3+90x2
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Solution

The correct option is B 20x4+88x3+90x2
We have,
y=(2x2+6x)(2x3+5x2)
Let,
u=2x2+6x and v=2x3+5x2
Using Product Rule:
d(uv)dx=udvdx+vdudx
dudx=4x+6 and dvdx=6x2+10x
Therefore
dydx=d(uv)dx=udvdx+ vdudx
=(2x2+6x)(6x2+10x)+(2x3+5x2)(4x+6)
=20x4+88x3+90x2

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