Question

How do you differentiate `f(x)=tan5x^3`?

Answer 1

`f'(x)=((v(u(x)))'=15x^2sec^2(5x^3)`

Explanation:

Differentiating `f(x)` is determined by applying the chain rule .
`" "`
Let `" "u(x)=5x^3" "and " "v(x)=tanx`
`" "`
Then,
`" "`
`f(x)=v(u(x))`
`" "`
Applying the chain rule for differentiation.
`" "`
`f'(x)=((v(u(x)))'=v'(u(x))xxu'(x)`
`" "`
`u'(x)=15x^2`
`" "`
`v'(x)=sec^2x" "then" "v'(u(x))=sec^2(5x^3)`
`" "`
Therefore,
`" "`
`f'(x)=((v(u(x)))'=v'(u(x))xxu'(x)`
`" "`
`f'(x)=((v(u(x)))'=sec^2(5x^3)xx15x^2`
`" "`
`f'(x)=((v(u(x)))'=15x^2sec^2(5x^3)`