Final answer to the problem
$\arcsin\left(x\right)^2\left(\arcsin\left(x\right)+\frac{3x}{\sqrt{1-x^2}}\right)$
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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
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\arcsin\left(x\right)^3$
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$\frac{d}{dx}\left(x\right)\arcsin\left(x\right)^3+x\frac{d}{dx}\left(\arcsin\left(x\right)^3\right)$
Learn how to solve problems step by step online. Find the derivative of xarcsin(x)^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\arcsin\left(x\right)^3. The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Taking the derivative of arcsine.
Final answer to the problem
$\arcsin\left(x\right)^2\left(\arcsin\left(x\right)+\frac{3x}{\sqrt{1-x^2}}\right)$
