What is the derivative of f(x)=(7-x)(5/(x^2)-8) ?

The derivative of f(x)=(7-x)(5/(x^2)-8) is (5x-70)/(x^3)+8

What is the first derivative of f(x)=(7-x)(5/(x^2)-8) ?

The first derivative of f(x)=(7-x)(5/(x^2)-8) is (5x-70)/(x^3)+8

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derivative of

f (x) = (7 - x) (\frac{5}{x ^{2}} - 8)

\frac{5 x - 70}{x ^{3}} + 8

Solution steps

\frac{d}{d x} ((7 - x) (\frac{5}{x ^{2}} - 8))

Apply the Product Rule:

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

f = 7 - x, g = \frac{5}{x ^{2}} - 8

= \frac{d}{d x} (7 - x) (\frac{5}{x ^{2}} - 8) + \frac{d}{d x} (\frac{5}{x ^{2}} - 8) (7 - x)

\frac{d}{d x} (7 - x) = - 1

\frac{d}{d x} (\frac{5}{x ^{2}} - 8) = - \frac{10}{x ^{3}}

= (- 1) (\frac{5}{x ^{2}} - 8) + (- \frac{10}{x ^{3}}) (7 - x)

Simplify

(- 1) (\frac{5}{x ^{2}} - 8) + (- \frac{10}{x ^{3}}) (7 - x) : \frac{5 x - 70}{x ^{3}} + 8

= \frac{5 x - 70}{x ^{3}} + 8

\frac{d y}{d x}, y = x^{2} + 1

\int e^{6 θ} sin (7 θ) d θ

x \to \infty lim ((3)^{x})

n = 1 \sum \infty \frac{n}{( n + 2 )}

- 5 t^{2} δ (t - 1)

What is the derivative of f(x)=(7-x)(5/(x^2)-8) ?
The derivative of f(x)=(7-x)(5/(x^2)-8) is (5x-70)/(x^3)+8
What is the first derivative of f(x)=(7-x)(5/(x^2)-8) ?
The first derivative of f(x)=(7-x)(5/(x^2)-8) is (5x-70)/(x^3)+8