Posted by **cynthia** on Saturday, February 25, 2012 at 9:50pm.

Let f(x)=(-3x^2+6)^4(9x^2+7)^14, Find f'(x).

f'(x)= (-3^2+6)^4 d/dx(9x^2+7)^14+(9x^2+7) d/dx(-3x^2+6)^4

=(-3x^2+6)x14(9x^2+7)^13 d/dx(9x^2+7)+(9x^2+7)^14x4(-3x^2+6)^3 d/dx(-3x^2+6)

=14(-3x+6)^4(9x^+7)^13 (18x)+ 4(9x^2+7)(-3x^2+6)^3 (-6x)

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**cynthia**, Saturday, February 25, 2012 at 9:59pm
i got stuck

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**MathMate**, Saturday, February 25, 2012 at 11:22pm
Start with the product rule, and take it slowly.

(d/dx)[(-3x^2+6)^4(9x^2+7)^14]

=(d/dx)[(-3x^2+6)^4](9x^2+7)^14 + (-3x^2+6)^4 (d/dx)[(9x^2+7)^14]

=4(-3x^2+6)^3 (d/dx)[-3x^2+6](9x^2+7)^14 + (-3x^2+6)^4*14(9x^2+7)^13(d/dx)[9x^2+7)

=4(-3x^2+6)^3 (-6x) + (-3x^2+6)^4*14(9x^2+7)^13 (18x)

Now take out the common factors (-3x^2+6)^3(9x^2+7)^13 to get

=(-3x^2+6)^3(9x^2+7)^13[4(-6x)(9x^2+7) + (-3x^2+6)14(18x)]

=(-3x^2+6)^3(9x^2+7)^13[-216x^3+168x + -756x^3+1512x]

=(-3x^2+6)^3(9x^2+7)^13[-972x^3+1344x]

=(-3x^2+6)^3(9x^2+7)^13(-12x)(81x^2-112)

=324x(x^2-2)^3(9x^2+7)^13(81x^2-112)

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**cynthia**, Monday, February 27, 2012 at 12:28am
hey how u get 324x?

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**MathMate**, Monday, February 27, 2012 at 9:01am
(-3x^2+6)^3(9x^2+7)^13(-12x)(81x^2-112)

=3^3(-12x)(-2+x^2)^3(9x^2+7)^13(81x^2-112)

=27*12x(x^2-2)^3(9x^2+7)^13(81x^2-112)

=324x(x^2-2)^3(9x^2+7)^13(81x^2-112)

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**cynthia**, Tuesday, February 28, 2012 at 1:25am
i got it thanks

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**MathMate**, Tuesday, February 28, 2012 at 7:23am
You're welcome! :)

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