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 December 15th, 2012, 04:10 AM #1 Newbie   Joined: Dec 2012 Posts: 8 Thanks: 0 First step of derivative, and also second derviative Hi Everyone, Quick question for most any math expert. If asked to find the first derivative of: f(x)=acos2x+b(sinx)^2 apparently the first step is f ' (x) = -2asin(2x) + 2bsinxcosx I do know that the derivative of cosx=-sinx and that the derivative of sinx=cosx. But I guess we dont use the product rule for the first term and then again for the second term. And I also have no idea where he got the -2 in the first term NOR do I understand where the cosx comes from in the second term. Can anyone offer a why? Also, regarding the second derivative, how does it go from f ' (x)= (b-2a)sin2x to f '' (x) = (b-2a)cox2X * 2 Any help is GREATLY appreciated!  December 15th, 2012, 10:05 AM   #2
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Re: First step of derivative, and also second derviative

Hi Everyone,

Quick question for most any math expert. If asked to find the first derivative of:

f(x)=acos2x+b(sinx)^2

apparently the first step is

f ' (x) = -2asin(2x) + 2bsinxcosx

Quote:
 And I also have no idea where he got the -2 in the first term
The chain rule. The derivative of cos is -sin. The derivative of 2x is 2.

The chain rule basically says, derivative of outside times derivative of inside.

So, we get

Quote:
 NOR do I understand where the cosx comes from in the second term
.

Again, the chain rule. Just like the derivative of is .

The derivative of the 'outside' is . The derivative of is

So, we get

Quote:
 Also, regarding the second derivative, how does it go from f ' (x)= (b-2a)sin2x to f '' (x) = (b-2a)cox2X * 2
The chain rule.

In other words, the chain rule says,

Let and write

So,

and

So, we have

Any help is GREATLY appreciated!  Tags derivative, derviative, step Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post dalo Math Software 1 March 17th, 2013 10:19 PM iamdaniel Academic Guidance 3 February 2nd, 2012 08:42 PM Weiler Differential Equations 1 January 31st, 2012 07:15 AM falcon Algebra 3 December 11th, 2009 03:44 PM Thefobkid Algebra 9 September 8th, 2008 04:44 AM

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