find the derivative of the function

Question

f(x)= tan (10x^2)

Answer 1

Use the function of a function or "chain" derivative rule.
Let u(x) = 10 x^2

f(x) = f{u(x)}
f(u) = tan u
df/dx = (df/du)*(du/dx)
= sec^2 u *(20 x)
= 20x *sec^2(10 x^2)