Differentiate Tan^-1y=x^3?
1 Answer
Sep 2, 2017
Explanation:
tan−1y=x3
Method 1 - No simplification
Differentiate as written. Recall that
11+y2⋅dydx=3x2
Solving for the derivative:
dydx=3x2(1+y2)
Let's write this all in terms of
dydx=3x2(1+tan2(x3))
Note that
dydx=3x2sec2(x3)
Method 2 - Simplification
Recall that
y=tan(x3)
dydx=sec2(x3)⋅ddxx3
dydx=3x2sec2(x3)