Question

How solve Derivatives of Trigonometric Functions? PLEASE HELP

I Do not remember how solve this........

Answer 1

I tried changing the `csc`:

Explanation:

I would use the Quotient and Chain Rule and remember that `csc(x)=1/sin(x)` so:
`f(x)=csc^2(7x^2)=1/sin^2(7x^2)`
So:
`f'(x)=-(2sin(7x^2) cos(7x^2)*14x)/(sin^4(7x^2))=-28x(cos(7x^2)/sin^3(7x^2))=-28xcsc^2(7x^2)cot(7x^2)`

Answer 2

Here I used Chain Rule successively:-

Explanation:

`f(x)` = `csc^2(7x^2)`
Now Differentiating both sides with respect to `x` successively we get:-
`f'(x)` = 2 `csc(7x^2).[ d/dx( csc 7x^2)]`
`rArr f'(x)` = `2csc(7x^2).[-csc(7x^2).cot(7x^2).d/dx(7x^2)]`

`rArr f'(x)` = `-2csc^2(7x^2).cot(7x^2).14x`

`rArr f'(x)` = `-28x.csc^2(7x^2).cot(7x^2)`