Final answer to the problem
$5\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$
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Step-by-step Solution
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- 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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1
The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function
$5\frac{d}{dx}\left(x^{\cos\left(2x\right)}\right)$
2
The derivative $\frac{d}{dx}\left(x^{\cos\left(2x\right)}\right)$ results in $\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$
$5\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$
Final answer to the problem
$5\left(-2x\sin\left(2x\right)\ln\left(x\right)+\cos\left(2x\right)\right)x^{\left(\cos\left(2x\right)-1\right)}$