Question

How do you differentiate `g(x)=cos(10^(2x))`?

Answer 1

`g'(x)=-2ln10sin(10^(2x))10^(2x)`

Explanation:

`•color(white)(x)d/dx(a^x)=a^xlna`

`"differentiate using the "color(blue)"chain rule"`

`"given "y=f(g(h(x)))" then"`

`dy/dx=f'(g(h(x))xxg'(h(x))xxh'(x)larr" chain rule"`

`rArrg'(x)=-sin(10^(2x))xxd/dx(10^(2x))`

`color(white)(rArrg'(x))=-sin(10^(2x))xx(10^(2x))ln10xxd/dx(2x)`

`color(white)(rArrg'(x))=-2ln10sin(10^(2x))10^(2x)`