Thursday

September 29, 2016
Posted by **cal** on Thursday, October 24, 2013 at 2:23pm.

f(x)= x^8√5-3x

- cal -
**Kuai**, Thursday, October 24, 2013 at 2:37pmf(x)= x^8√5-3x

f'(x) = 8x^7√5-3 - cal -
**cal**, Thursday, October 24, 2013 at 2:46pmbut the ans is f(x)= x^7(80-51x)/2√5-3x

- cal -
**Jai**, Thursday, October 24, 2013 at 2:49pmIf you mean f(x) = x^8√(5-3x), then

f'(x)

= (8x^7)*√(5-3x) + (-3/2)*(x^8) / √(5-3x) - cal -
**cal**, Thursday, October 24, 2013 at 2:56pmam lost

- cal -
**Jai**, Thursday, October 24, 2013 at 3:07pmRecall the chain rule. If two expressions which are functions of x are multiplied, we do the following:

h(x) = f(x)*g(x)

h'(x) = f'(x)*g(x) + f(x)*g'(x)

As we can see, the derivative of h(x) is the derivative of f(x) multiplied by the original g(x), plus the derivative of g(x) multiplied by the original f(x).

For example,

h(x) = 2x * ln(x)

We know that

derivative of 2x = 2, and

derivative of ln(x) = 1/x. Thus

h'(x) = 2*ln(x) + (2x)*(1/x)

In the problem, f(x) = x^8√(5-3x). We can rewrite this as,

f(x) = (x^8) * (5-3x)^(1/2)

We know that

the derivative of x^8 = 8x^7

the derivative of (5-3x)^(1/2) = (1/2)(-3)(5-3x)^(-1/2)

Using chain rule, you'll get

f'(x) = (8x^7)*(5-3x)^(1/2) + (x^8)*(-3/2)*(5-3x)^(-1/2)

If you simplify this, you'll get the answer that you typed in there:

f'(x) = x^7(80-51x) / 2√(5-3x)

Hope this helps :) - cal -
**cal**, Thursday, October 24, 2013 at 3:13pmthanks jai