# What is the derivative of this function #y=sec^-1(x^7)#?

##### 1 Answer

Dec 2, 2016

#### Explanation:

When tackling the derivative of inverse trig functions. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. If you can remember the inverse derivatives then you use the chain rule.

Let

Differentiate Implicitly:

# secytanydy/dx = 7x^6 #

# :. x^7tanydy/dx = 7x^6 #

# :. tanydy/dx = 7/x # # (x!=0)# .... [1]

Using the

# tan^2y+1=sec^2y #

# :. tan^2y+1=(x^7)^2 #

# :. tan^2y=x^14-1 #

# :. tany=sqrt(x^14-1) #

Substituting into [1]