Question

diffrentiate sinx/cosx

Answer 1

Hiii
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sinx/cosx = tanx
dy/dx=tanx
=sec^2x
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hope it helps u...
plzz mark as brainliest....

Answer 2

Hey there!

We are asked to differentiate sinx / cosx with respective to x.

While studying differentiation, We usually learn that

d(tanx)/dx = sec²x.

As the question asks about sinx/cosx that is tanx. This is a direct answer.

But, It can also be derived. Let's see how.


$\frac{d }{dx} ( \frac{u}{v} ) = \frac{ v \frac{d}{dx} (u) - u \frac{d}{dx} (v)}{ {v}^{2}}$


So,
d/dx( sinx / cosx)

= cosx * d/dx( sinx) - sinx * d/dx ( cosx) / cos²x

= cosx( cosx) - (sinx) ( - sinx) / cos²x

= cos²x + sin²x / cos²x

= 1/cos²x

= sec²x

Therefore, d/dx ( sinx/cosx) = sec²x.

Here we have used two results that are,

d/dx(sinx) = cosx

d/dx(cosx) = -sinx.