Question

first derivative of tan (1/4 pi - 1/2x )?

Answer 1

The chain rule lets you take a complicated looking function and turn it into derivatives of two functions you know. So in this case, we look at this and say:

We can find the derivative of tan(x) and we can take the derivative of (pi/4 - x/2). So if one is inside the other then we can take that derivative too by multiplying the derivative of the outside by the inside thing. I'll show you:

\[\frac{ d }{ dx } [ \tan(\frac{ \pi }{ 4 } - \frac{ x }{ 2 })] = \sec^2(\frac{ \pi }{ 4 } - \frac{ x }{ 2 }) *(\frac{ 1 }{ 2 })\]

So we took the derivative of tangent without touching the stuff inside, which is sec^2 of the stuff inside. Then we multiply it by the derivative of the inside stuff, which is just the derivative of pi/4 which is 0 since it's constant and x/2 is just 1/2.

Answer 2

pi/4 is 45..

Answer 3

ahh!! okay okay. Thanks =))

Answer 4

Haha yeah no problem if you feel like the chain rule doesn't make sense, I suggest you make sure you can do it with functions you already know the derivative of... but from a different perspective! What about taking the derivative of:

y=x^4

What if you look at that as being:

y=(x^2)^2

This is the exact same thing, except this lets you look at it from the chain rule perspective!

y'=2(x^2)*(2x)=4x^3

Huzzah! It's all consistent! You could even do the product rule this way too.

y=x^4=x^3*x

y'=3x^2*x+x^3*1=4x^3

Just some food for thought.