will we use chain rule when ever we have to find derivative of a function with respect to itself ?

Question

abb0t · Answer

for example, if you have: 

$\large sin^{200}(8x)$ this is the same thing as saying $\large [sin(8x)]^{200}$ in which case you are using chain rule. The derivative of the outside FIRST mutiplied by derivative of the inside. So your outside is the 200, your inside is ur sin, and then inside of ur sine, you have (8x)

So you would get: $ large (200 \times [sin(8x)]^{200-1} \times cos(8x) \times 8$
you see how i did that?

anonymous · Answer

yeah you used d\dx(f^n)= nf^n-1  *   d\dx(f)

abb0t · Answer

yes

anonymous · Answer

but what will be derivative of tanx w.r.t to tan x ? it will be 1 by using  chain rule which is my question ?

abb0t · Answer

so $tan(tan(x))$??? sme as chain rule. derivative of outside tan times derivative of inside tangent.

abb0t · Answer

its the same with $cos(cos(cos(cos(cos(cos(x)))))))$