Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\cos\left(x\right)$ and $g=\csc\left(x\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\cos\left(x\right)\right)\csc\left(x\right)+\cos\left(x\right)\frac{d}{dx}\left(\csc\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of cos(x)csc(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\cos\left(x\right) and g=\csc\left(x\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Applying the trigonometric identity: \sin\left(\theta \right)\csc\left(\theta \right) = 1. Taking the derivative of cosecant function: \frac{d}{dx}\left(\csc(x)\right)=-\csc(x)\cdot\cot(x)\cdot D_x(x).
