Final answer to the problem
$1=\frac{6}{\left(6x+3\right)\sqrt{\left(\frac{6x+3}{5}\right)^2-1}}$
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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 implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable
$\frac{d}{dx}\left(x\right)=\frac{d}{dx}\left(-\mathrm{arccsc}\left(\frac{6x+3}{5}\right)\right)$
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$\frac{d}{dx}\left(x\right)=\frac{d}{dx}\left(-\mathrm{arccsc}\left(\frac{6x+3}{5}\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(x=-arccsc((6x+3)/5)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Taking the derivative of arccosecant.
Final answer to the problem
$1=\frac{6}{\left(6x+3\right)\sqrt{\left(\frac{6x+3}{5}\right)^2-1}}$
