Derivative of a arctan

Question

I am not sure on how to even start, I know how to do simpler derivative but not a complex one like this.

I need to find $\frac{d(x^2 arctan(5x))}{dx}$

Use the product rule, and the fact that $\frac{d}{dx} \arctan(kx)=\frac{k}{k^2x^2+1}$. — lemon, Oct 17 '14 at 09:36

score 2 · Answer 1 · answered Oct 17 '14 at 09:36

2

Here we go. You know that $\arctan'(x) = \frac1{1+x^2}$. Then the derivative of $$ \arctan(5x) $$ is $$ 5\frac1{1+(5x)^2} $$ Then use the product rule.

answered Oct 17 '14 at 09:36

mookid

28,236

score 1 · Answer 2 · edited Oct 17 '14 at 10:56

1

$$\displaystyle \frac{d(x^2\arctan(5x))}{dx}=\\2x\arctan(5x)+x^2\left(\frac{5}{1+25x^2}\right)$$ by product rule and derivative of $\arctan$ function.

edited Oct 17 '14 at 10:56

beep-boop

11,595

answered Oct 17 '14 at 09:39

Derivative of a arctan

2 Answers2