Question

Find the derivative of arctan(10x)

Answer 1

dy/dx=10/(1+100x^2)

Explanation:

Let y=arctan(10x).

Then tan(y)=10x.

Differentiate both sides:

sec^2(y)×dy/dx=10

Divide both sides by sec^2(y):

dy/dx=10/sec^2(y)

By a Pythagorean identity:

dy/dx=10/(1+tan^2(y))

Recall tan(y)=10x:

dy/dx=10/(1+(10x)^2)

dy/dx=10/(1+100x^2)

Answer 2

`\frac{10}{100x {}^(2) + 1 }`