Homework Help: math-check my work

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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