Final answer to the problem
$\frac{8}{3\sqrt{1-\left(\frac{8x+5}{3}\right)^2}}$
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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
Taking the derivative of arcsine
Learn how to solve differential calculus problems step by step online.
$\frac{1}{\sqrt{1-\left(\frac{8x+5}{3}\right)^2}}\frac{d}{dx}\left(\frac{8x+5}{3}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of arcsin((8x+5)/3). Taking the derivative of arcsine. The derivative of a function multiplied by a constant (\frac{1}{3}) is equal to the constant times the derivative of the function. Multiplying fractions \frac{1}{\sqrt{1-\left(\frac{8x+5}{3}\right)^2}} \times \frac{1}{3}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Final answer to the problem
$\frac{8}{3\sqrt{1-\left(\frac{8x+5}{3}\right)^2}}$
