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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(1-\sin\left(x\right)^2\right)\csc\left(x\right)+\left(1-\sin\left(x\right)^2\right)\frac{d}{dx}\left(\csc\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule (1-sin(x)^2)csc(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. Taking the derivative of cosecant function: \frac{d}{dx}\left(\csc(x)\right)=-\csc(x)\cdot\cot(x)\cdot D_x(x). Simplify the product -(1-\sin\left(x\right)^2). The derivative of the linear function is equal to 1.