Final answer to the problem
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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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\arctan\left(x\right)$ and $g=\cos\left(5x\right)$
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$\frac{d}{dx}\left(\arctan\left(x\right)\right)\cos\left(5x\right)+\arctan\left(x\right)\frac{d}{dx}\left(\cos\left(5x\right)\right)$
Learn how to solve equations problems step by step online. Find the derivative of arctan(x)cos(5x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\arctan\left(x\right) and g=\cos\left(5x\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). The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.
