Question

If y=sinx/cosx then dy/dx=
Explain briefly.​

Answer 1

Answer : sec²x

Solution :

Given that :

y = sinx/cosx

As we know that :

sinA/cosA = tanA

Then, y = tanx

On differentiate w.r. to x both the sides :

dy/dx = d(tanx)/dx

=> dy/dx = sec²x

I hope it will be helpful for you ☺️

Fóllòw MË ❤️

Answer 2

Answer:. Sec^2x

Explanation --------->

Since, y=sinx/cosx

Soi, by differentiating both sides w.r..t x

dy/dx=d(sinx/cosx)/dx

By quotient rule ,

d(sinx/cosx)ldx=

(d(sinx)/dx.cosx-d(cosx)/dx.sinx)/cos^2x

Now we get

(cosx.cosx-(-sinx).sinx)/cos^2x

As,d(sinx)/dx=cosx.& d(cosx)/dx= -sinx

So,

=(cos^2x+sin^2x))/cos^2x

=1/cos^2x

=sec^2x. (As 1/cosx=secx)

I hope that it will helps u very much.

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