What is the derivative of f(x)=(4-x)(2/(x^2)-3) ?

The derivative of f(x)=(4-x)(2/(x^2)-3) is (2x-16)/(x^3)+3

What is the first derivative of f(x)=(4-x)(2/(x^2)-3) ?

The first derivative of f(x)=(4-x)(2/(x^2)-3) is (2x-16)/(x^3)+3

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derivative of

f (x) = (4 - x) (\frac{2}{x ^{2}} - 3)

\frac{2 x - 16}{x ^{3}} + 3

Solution steps

\frac{d}{d x} ((4 - x) (\frac{2}{x ^{2}} - 3))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4 - x, g = \frac{2}{x ^{2}} - 3

= \frac{d}{d x} (4 - x) (\frac{2}{x ^{2}} - 3) + \frac{d}{d x} (\frac{2}{x ^{2}} - 3) (4 - x)

\frac{d}{d x} (4 - x) = - 1

\frac{d}{d x} (\frac{2}{x ^{2}} - 3) = - \frac{4}{x ^{3}}

= (- 1) (\frac{2}{x ^{2}} - 3) + (- \frac{4}{x ^{3}}) (4 - x)

Simplify

(- 1) (\frac{2}{x ^{2}} - 3) + (- \frac{4}{x ^{3}}) (4 - x) : \frac{2 x - 16}{x ^{3}} + 3

= \frac{2 x - 16}{x ^{3}} + 3

What is the derivative of f(x)=(4-x)(2/(x^2)-3) ?
The derivative of f(x)=(4-x)(2/(x^2)-3) is (2x-16)/(x^3)+3
What is the first derivative of f(x)=(4-x)(2/(x^2)-3) ?
The first derivative of f(x)=(4-x)(2/(x^2)-3) is (2x-16)/(x^3)+3