Differential calculus that boils down to a mistake in Product Rule? Chain rule? With Sin'(x) portion and other goodies

[JohnLockwood]

Hi,

I was working this Kahn Academy exercise while self-studying differential calculus and boiled my inability to get the right answer down to this piece of product rule (chain rule?) that I wasn't getting somehow:

[math]\frac{d}{dt}[80sin(0.6t)] = 48 cos(0.6t).[/math]
I think I'm OK, on the product rule and chain rule general forms, and I get that 80*0.6 = 48 and that

[math]\frac{d}{dx}[sin(x)] = cos(x)[/math]
but I'm not getting how the whole expression

[math]\frac{d}{dt}[80sin(0.6t)] = 48 cos(0.6t).[/math]
is correct rather than my (incorrect):

[math]\frac{d}{dt}[80sin(0.6t)] = 80 cos(0.6t).[/math]
Clearly, I'm missing an important piece or doing something wrong, but at this point, I'm not getting what that is. Am I missing a simple trig rule or something? Thanks for any insights you might provide.

 

[Dr.Peterson]

Hi,

I was working this Kahn Academy exercise while self-studying differential calculus and boiled my inability to get the right answer down to this piece of product rule (chain rule?) that I wasn't getting somehow:

[math]\frac{d}{dt}[80sin(0.6t)] = 48 cos(0.6t).[/math]
I think I'm OK, on the product rule and chain rule general forms, and I get that 80*0.6 = 48 and that

[math]\frac{d}{dx}[sin(x)] = cos(x)[/math]
but I'm not getting how the whole expression

[math]\frac{d}{dt}[80sin(0.6t)] = 48 cos(0.6t).[/math]
is correct rather than my (incorrect):

[math]\frac{d}{dt}[80sin(0.6t)] = 80 cos(0.6t).[/math]
Clearly, I'm missing an important piece or doing something wrong, but at this point, I'm not getting what that is. Am I missing a simple trig rule or something? Thanks for any insights you might provide.

What do you get for [imath]\frac{d}{dt}[\sin(0.6t)][/imath]? I think you're missing the chain rule, where the inner function is 0.6t, and the outer function is sin.

 

[JohnLockwood]

What do you get for [imath]\frac{d}{dt}[\sin(0.6t)][/imath]? I think you're missing the chain rule, where the inner function is 0.6t, and the outer function is sin.

Ah yes, I think I see my mistake now, and you're right. That's what I'm missing. That gives

[math]cos(0.6t) \times .06[/math]
Multiplying by the original 80, we end up with:

[math]80 \times 0.6 \times cos(0.6t) = 48cos(0.6t)[/math]
I'll go practice on some similar chain rule problems. Thanks for the help!