Question Number 66099 by olalekan2 last updated on 09/Aug/19
![differentiate y=10^(1−sin^2 3x)](https://www.tinkutara.com/question/Q66099.png)
$${differentiate}\:{y}=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \mathrm{3}{x}} \\ $$
Commented by mathmax by abdo last updated on 09/Aug/19
![y(x) =10^(1−sin^2 (3x)) ⇒y(x) =e^((1−sin^2 (3x))ln(10)) ⇒ y^′ (x) =ln(10)(−6cos(3x) sin(3x))y(x)=−6ln(10)cos(3x)sin(3x)y(x)](https://www.tinkutara.com/question/Q66118.png)
$${y}\left({x}\right)\:=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)} \:\Rightarrow{y}\left({x}\right)\:={e}^{\left(\mathrm{1}−{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)\right){ln}\left(\mathrm{10}\right)} \:\Rightarrow \\ $$$${y}^{'} \left({x}\right)\:={ln}\left(\mathrm{10}\right)\left(−\mathrm{6}{cos}\left(\mathrm{3}{x}\right)\:{sin}\left(\mathrm{3}{x}\right)\right){y}\left({x}\right)=−\mathrm{6}{ln}\left(\mathrm{10}\right){cos}\left(\mathrm{3}{x}\right){sin}\left(\mathrm{3}{x}\right){y}\left({x}\right) \\ $$