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2 years ago

What is the derivative of f(x)= 1/5(x^2 + 2)^5/2?

Mathematics

2 answers:

vlabodo [156]2 years ago

8 0

Answer:

x(x^2+2)^3/2

Step-by-step explanation:

y'=1/2(x^2+2)^3/2.2x

= x(x^2+2)^3/2

vlada-n [284]2 years ago

3 0

$f(x)=\cfrac{1}{5}(x^2+2)^{\frac{5}{2}}\implies \cfrac{df}{dx}=\cfrac{1}{5}\stackrel{\textit{chain~rule}}{\left[\cfrac{5}{2}(x^2+2)^{\frac{3}{2}} \cdot (2x) \right]} \\\\\\ \cfrac{df}{dx}=(x^2+2)^{\frac{3}{2}}(x)\implies \cfrac{df}{dx}=x\sqrt{(x^2+2)^3}$

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Answer:

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Step-by-step explanation:

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