How do you find the derivative of $f (x) = - 4 x^{5} + 3 x^{2} - \frac{5}{x^{2}}$ $f(x)=-4x^5+3x^2-5/x^2$ ?

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How do you find the derivative of $f (x) = - 4 x^{5} + 3 x^{2} - \frac{5}{x^{2}}$ $f(x)=-4x^5+3x^2-5/x^2$ ?

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Answer 1 · 2017-04-09T19:37:39

$\frac{d}{d x} f (x) = \frac{- 20 x^{16} + 6 x^{5} - 10 x}{x^{4}}$ $d/(d x) f(x)=(-20x^(16)+6x^5-10x)/x^4$

Explanation:

$f (x) = - 4 x^{5} + 3 x^{2} - \frac{5}{x^{2}}$ $f(x)=-4x^5+3x^2-5/x^2$

$\frac{d}{d x} f (x) = \frac{d}{d x} (- 4 x^{5}) + \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (\frac{5}{x^{2}})$ $d/(d x) f(x)=color(red)(d/(d x)( -4x^5))+color(blue)( d/(d x)(3x^2))-color(green)(d/(d x)(5/x^2))$

$\frac{d}{d x} (- 4 x^{5}) = - 20 x^{4}$ $color(red)(d/(d x)( -4x^5))=-20x^4$

$\frac{d}{d x} (3 x^{2}) = 6 x$ $color(blue)(d/(d x)(3x^2))=6x$

$\frac{d}{d x} (\frac{5}{x^{2}}) = \frac{0 \cdot x^{2} - 2 x \cdot 5}{{(x^{2})}^{2}} = \frac{- 10 x}{x^{4}}$ $color(green)(d/(d x)(5/x^2))=(0*x^2-2x*5)/(x^2)^2=(-10x)/x^4$

$\frac{d}{d x} f (x) = - 20 x^{4} + 6 x - \frac{10 x}{x^{4}}$ $d/(d x) f(x)=-20x^4+6x-(10x)/x^4$

$\frac{d}{d x} f (x) = \frac{- 20 x^{16} + 6 x^{5} - 10 x}{x^{4}}$ $d/(d x) f(x)=(-20x^(16)+6x^5-10x)/x^4$

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How do you find the derivative of $f (x) = - 4 x^{5} + 3 x^{2} - \frac{5}{x^{2}}$ $f(x)=-4x^5+3x^2-5/x^2$ ?

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Explanation:

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How do you find the derivative of $f (x) = - 4 x^{5} + 3 x^{2} - \frac{5}{x^{2}}$ $f(x)=-4x^5+3x^2-5/x^2$ ?