Final answer to the problem
$k\left(\arcsin\left(3x-1\right)+3x\frac{1}{\sqrt{1-\left(3x-1\right)^2}}\right)$
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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
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$k\frac{d}{dx}\left(x\arcsin\left(3x-1\right)\right)$
Learn how to solve problems step by step online. Find the derivative of kxarcsin(3x-1). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\arcsin\left(3x-1\right). The derivative of the linear function is equal to 1. Taking the derivative of arcsine.
Final answer to the problem
$k\left(\arcsin\left(3x-1\right)+3x\frac{1}{\sqrt{1-\left(3x-1\right)^2}}\right)$
