How do you differentiate $f (x) = x \sqrt{4 - x^{2}}$ $f(x) =x sqrt(4-x^2)$ using the product rule?

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How do you differentiate $f (x) = x \sqrt{4 - x^{2}}$ $f(x) =x sqrt(4-x^2)$ using the product rule?

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Answer 1 · 2018-02-15T08:10:04

$- \frac{x^{2}}{\sqrt{4 - x^{2}}} + \sqrt{4 - x^{2}}$ $-x^2/sqrt(4-x^2)+sqrt(4-x^2)$

Explanation:

$\frac{d}{d x} (x \sqrt{4 - x^{2}}) = x \frac{d}{d x} (\sqrt{4 - x^{2}}) + \frac{d}{d x} (x) \sqrt{4 - x^{2}} = x (\frac{1}{2} {(4 - x^{2})}^{- \frac{1}{2}} (- 2 x) + 1 \sqrt{4 - x^{2}} = - \frac{x^{2}}{\sqrt{4 - x^{2}}} + \sqrt{4 - x^{2}}$ $d/dx(xsqrt(4-x^2) )=xd/dx(sqrt(4-x^2 ))+d/dx(x)sqrt(4-x^2)=x(1/2(4-x^2)^(-1/2)(-2x)+1sqrt(4-x^2)=-x^2/sqrt(4-x^2)+sqrt(4-x^2)$

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How do you differentiate $f (x) = x \sqrt{4 - x^{2}}$ $f(x) =x sqrt(4-x^2)$ using the product rule?

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Explanation:

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How do you differentiate f(x) =x sqrt(4-x^2) f(x)=x√4−x2f(x) =x sqrt(4-x^2) using the product rule?

1 Answer

Explanation:

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How do you differentiate $f (x) = x \sqrt{4 - x^{2}}$ $f(x) =x sqrt(4-x^2)$ using the product rule?