Question

derivative y = arctan⁴(3x⁵)

Answer 1

Remind that the derivative of the composition of functions$f(g(x))$ is: $f'_x(g(x))=f'_g(g(x))g'(x)$. Thus, we get: $y'=\frac{4(\arctan^3(3x^5))(3x^5)'}{1+9x^{10}}=\frac{60x^4\arctan^3(3x^5)}{1+9x^{10}}.$

The answer is: $y'=\frac{60x^4\arctan^3(3x^5)}{1+9x^{10}}$