Question

If f(x) = 5x^4 tan^-1x, find f '(x).

Answer 1

\[\large\rm f(x) = 5x^4 \arctan x\]Start by setting up your product rule:\[\large\rm f'(x) = \color{royalblue}{\left(5x^4\right)'}\arctan x+5x^4\color{royalblue}{\left( \arctan x\right)'}\]And from there, just a lil bit of work.
Power rule on one, special derivative for the other, ya?

Answer 2

20x^3tan^-1x + 5x^4 1/sqrt(1-x^2)

Answer 3

hint:
\[\frac{{d\arctan x}}{{dx}} = \frac{1}{{1 + {x^2}}}\]

Answer 4

ok i got 20x3tan-1x + 5x4 1/1+x^2

Answer 5

correct! After a substitution, we get:
\[f'\left( x \right) = 20{x^3}\arctan x + \frac{{5{x^4}}}{{1 + {x^2}}}\]

Answer 6

thank you!