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Simplify the expression $\left(x+\cos\left(2x\right)\right)^{\csc\left(3x\right)}$

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Derivative

$\frac{d}{dx}\left(\left(x+\cos\left(2x\right)\right)^{\csc\left(3x\right)}\right)=\frac{y^{\prime}}{y}=-3\csc\left(3x\right)\cot\left(3x\right)\ln\left(x+\cos\left(2x\right)\right)+\csc\left(3x\right)\frac{1}{x+\cos\left(2x\right)}\left(1-2\sin\left(2x\right)\right)$ See full solution

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (x+cos2x)^csc3x using the definitionSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

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Main Topic: Product Rule of differentiation

The product rule is a formula used to find the derivatives of products of two or more functions. It may be stated as $(f\cdot g)'=f'\cdot g+f\cdot g'$

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