Final Answer
$\frac{-\sin\left(x\right)\left(1+\sin\left(x\right)\right)^2-2\cos\left(x\right)^2\left(1+\sin\left(x\right)\right)}{\left(1+\sin\left(x\right)\right)^{4}}$
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Step-by-step Solution
Specify the solving method
1
Find the ($1$) derivative
$\frac{\cos\left(x\right)}{\left(1+\sin\left(x\right)\right)^2}$
2
Find the ($2$) derivative
$\frac{-\sin\left(x\right)\left(1+\sin\left(x\right)\right)^2-2\cos\left(x\right)^2\left(1+\sin\left(x\right)\right)}{\left(1+\sin\left(x\right)\right)^{4}}$
Final Answer
$\frac{-\sin\left(x\right)\left(1+\sin\left(x\right)\right)^2-2\cos\left(x\right)^2\left(1+\sin\left(x\right)\right)}{\left(1+\sin\left(x\right)\right)^{4}}$