Can you differentiate inverse trig functions implicitly ?

3 years ago

1 Reply

1677 views

Genevieve Lebsack

1 Answer

Liz R Verified Sherpa Tutor ✓

Enthusiastic, Patient, Maths Teacher with 30 Years Experience.

5 reviews

Yes -this is the method used.

If y=arcsin x then x=siny

Differentiating both sides with respect to x gives

1=cos y (dy/dx).

Rearranging gives dy/dx = 1/cos y.

However cos y = sqrt (1 - sin²y) = sqrt (1- x²) and hence

dy/dx=1/sqrt (1-x²)

I'm available for 1:1 private online tuition!

Think you can help?

Need an A-Level Maths tutor?

Get started with a free online introductions with an experienced and qualified online tutor on Sherpa.