`f(x) = tanh(4x^2+3x)` Find the derivative of the function

`f(x) = tanh(4x^2+3x)`

The derivative formula of hyperbolic tangent is

• `d/dx [tanh(u)] = sec h^2(u)*(du)/dx`

Applying this formula, the derivative of the function will be

`f'(x)=d/dx[tanh(4x^2+3x)]`

`f'(x) = s e c h^2(4x^2+3x)*d/dx(4x^2+3x)`

`f'(x) = sec h^2(4x^2+3x)*(8x+3)`

`f'(x)=(8x+3)sec h^2(4x^2+3x)`

Therefore, the derivative of the given function is `f'(x)=(8x+3)sec h^2(4x^2+3x)` .