Final answer to the problem
$\frac{\mathrm{sinh}\left(\ln\left(x-t\right)\right)}{x-t}$
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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 hyperbolic cosine
$\frac{d}{dx}\left(\ln\left(x-t\right)\right)\mathrm{sinh}\left(\ln\left(x-t\right)\right)$
Learn how to solve sum rule of differentiation problems step by step online.
$\frac{d}{dx}\left(\ln\left(x-t\right)\right)\mathrm{sinh}\left(\ln\left(x-t\right)\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of cosh(ln(x-t)). Taking the derivative of hyperbolic cosine. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Multiply the fraction by the term .
Final answer to the problem
$\frac{\mathrm{sinh}\left(\ln\left(x-t\right)\right)}{x-t}$
