$\frac{d}{dx}\left(\frac{\sec\left(x\right)}{1+\cos\left(x\right)^2}\right)=\frac{\sec\left(x\right)\tan\left(x\right)\left(1+\cos\left(x\right)^2\right)+2\cos\left(x\right)\sin\left(x\right)\sec\left(x\right)}{\left(1+\cos\left(x\right)^2\right)^2}$
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