# Differentiate Tan^-1y=x^3?

##### 1 Answer

#### Explanation:

#tan^-1y=x^3#

**Method 1 - No simplification**

Differentiate as written. Recall that

#1/(1+y^2)*dy/dx=3x^2#

Solving for the derivative:

#dy/dx=3x^2(1+y^2)#

Let's write this all in terms of

#dy/dx=3x^2(1+tan^2(x^3))#

Note that

#dy/dx=3x^2sec^2(x^3)#

**Method 2 - Simplification**

Recall that

#y=tan(x^3)#

#dy/dx=sec^2(x^3)*d/dxx^3#

#dy/dx=3x^2sec^2(x^3)#