Final answer to the problem
$\frac{e^x}{\sqrt{x}}+\frac{-e^x}{2\sqrt{x^{3}}}$
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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
Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$
Learn how to solve quotient rule of differentiation problems step by step online.
$\frac{d}{dx}\left(e^x\cdot x^{- \frac{1}{2}}\right)$
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx((e^x)/(x^(1/2))). Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Multiply the fraction and term in - \frac{1}{2}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^x and g=x^{-\frac{1}{2}}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Final answer to the problem
$\frac{e^x}{\sqrt{x}}+\frac{-e^x}{2\sqrt{x^{3}}}$
