Posted by **Scott** on Friday, November 23, 2007 at 1:52pm.

Differentiate y=x(x4+5)3

d/dx = [x(x4+5)3]

d/dx = [f(x)g(x)] = f(x)g’(x)+g(x)f’(x)

d/dx = [x(x4+5)3] = x • d/dx (x4+5)3 + (x4+5)3 • d/dx x

g’(x) = d/dx (x4+5)3 = 3(x4+5)2 • 4x

f’(x) = d/dx (x) = 1

= (x) • 3(x4+5)2 • 4x + (x4+5)3 • 1 (factor out the common form (x4+5)2 )

= (x4+5)2 [(x)(3)(4x)+ (x4+5)]

=(x4+5)2 (12x2+x4+5) (answer I got)

The right answer =(x4+5)2 (13x4+5)

Just trying to see where I went wrong.

- math-check my work -
**bobpursley**, Friday, November 23, 2007 at 3:01pm
Shouldn't g'= 3(x^4+5)^2 * 4x^3 ?

- math-check my work -
**drwls**, Friday, November 23, 2007 at 3:23pm
It is hard to read your work with the exponents not raised or indicated by a ^ symbol. There is a mistake where you take the derivative of (x^4+5)^3. You used the "function of a function" or "chain" rule incorrectly.

Here is what I get:

y = x(x^4 +5)^3

Let f(x) = x and g(x) = (x^4+5)^3

dy/dx = (x^4+5)^3 + 3x(x^4+5)^2*4x^3

= (x^4+5)^2 *[(x^4+5) + 12x^4]

= (x^4+5)^2 *(13x^4+ 5)

- math-check my work -
**Anonymous**, Tuesday, November 27, 2007 at 9:30pm
8 . 4

- - 2 = -

6 . 3

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