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 $f=\sin\left(x\right)$ and $g=\cos\left(3x+1\right)$
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$\frac{d}{dx}\left(\sin\left(x\right)\right)\cos\left(3x+1\right)+\sin\left(x\right)\frac{d}{dx}\left(\cos\left(3x+1\right)\right)$
Learn how to solve problems step by step online. Find the derivative of sin(x)cos(3x+1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=\cos\left(3x+1\right). The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. 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 a sum of two or more functions is the sum of the derivatives of each function.
