Question

What is the slope of the line tangent to the graph of y = arctan(3x) at x = 1?

Answer 1

Slope is `3/10`

Explanation:

Slop of a line, tangent to a curve `y=f(x)` at `x=x_0` is `f'(x_0)`.

As `d/(dx) arctanx=1/(1+x^2)`

for `f(x)=arctan(3x)`, using chain rule

`f'(x)=1/(1+(3x)^2)xx3=3/(1+9x^2)`

and as we need slope of tangent at `x=1`

Slope is `3/(1+9*1^2)=3/(1+9)=3/10`