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)

- COLLEGE CALCULUS. HELP! -
**cynthia**, Saturday, February 25, 2012 at 9:59pm
i got stuck

- COLLEGE CALCULUS. HELP! -
**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)

- COLLEGE CALCULUS. HELP! -
**cynthia**, Monday, February 27, 2012 at 12:28am
hey how u get 324x?

- COLLEGE CALCULUS. HELP! -
**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)

- COLLEGE CALCULUS. HELP! -
**cynthia**, Tuesday, February 28, 2012 at 1:25am
i got it thanks

- COLLEGE CALCULUS. HELP! -
**MathMate**, Tuesday, February 28, 2012 at 7:23am
You're welcome! :)

## Answer This Question

## Related Questions

- college algebra - y intercept: 3x^2+18x 0=3x^2+18x from here im lost
- math - when I have (2x^(3)-18x)-(2x^(3)) / (x^(2)-9) am I suppose to be left ...
- college algebrall - find the vertex and line of symmetry f(x)=x^2-6x+8 f(x)=3x^2...
- Math - Find the Least Common multiple of the two expressions: 24x^2-96 & 18x^2+...
- Calculus - Taylor - could you please help me with solving this problem? #1) Find...
- calculus-answer check - Deermine the derivative of f(x)=[(3x^2+1)^3+1]^2. ...
- Math - 9x^2+16y^2-18x+64y-71=0 find the coordinates of the center, the foci, and...
- Algebra - checking problem Use FOIL to multiply: (6x – 1)(3x – 4) 6x*3x + 6x*(-4...
- calculus - f(x)=(9x^2–8)^6(4x^2–5)^11 Find f'(x) I got (9x^2-8)^6 *11(4x^2-3)^...
- calculus - Find the volume generated by revolving the region bounded by y=18x-3x...

More Related Questions