Derivative - Inverse Trigonometric Functions, 3

Category: Differential Calculus, Trigonometry

"Publish in Suisun City, California, USA"

Prove that

Solution:

Consider the given equation above

Let

Take tangent on both sides of the equation, we have

Take the derivative on both sides of the equation with respect to x, we have 

Next, we need to eliminate sec² y in the equation. We know that  

but

Hence, the above equation becomes

Finally, the equation becomes

but

Therefore,

 

Derivative - Inverse Trigonometric Functions, 2

Category: Differential Calculus, Trigonometry

"Published in Suisun City, California, USA"

Prove that

Solution:

Consider the given equation above

Let

Take cosine on both sides of the equation, we have

Take the derivative on both sides of the equation with respect to x, we have

Next, we need to eliminate sin y in the equation. We know that 

but

Hence, the above equation becomes

Finally, the equation becomes

but

Therefore,

Derivative - Inverse Trigonometric Functions

Category: Differential Calculus, Trigonometry

"Published in Suisun City, California, USA"

Prove that

Solution:

Consider the above equation

Let

Take sine on both sides of the equation, we have

Take the derivative on both sides of the equation with respect to x, we have

Next, we need to eliminate cos y in the equation. We know that 

but

Hence, the above equation becomes

Finally, the equation becomes

but

Therefore,