Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the derivative
- 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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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\ln\left(\sqrt{x+1}\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(x\right)\ln\left(\sqrt{x+1}\right)+x\frac{d}{dx}\left(\ln\left(\sqrt{x+1}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of xln((x+1)^(1/2)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\ln\left(\sqrt{x+1}\right). The derivative of the linear function is equal to 1. 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 power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
