What is the derivative of 7x^{-6}-5x^{-3} ?

The derivative of 7x^{-6}-5x^{-3} is -(42)/(x^7)+(15)/(x^4)

What is the first derivative of 7x^{-6}-5x^{-3} ?

The first derivative of 7x^{-6}-5x^{-3} is -(42)/(x^7)+(15)/(x^4)

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\frac{d}{d x} (7 x^{- 6} - 5 x^{- 3})

- \frac{42}{x ^{7}} + \frac{15}{x ^{4}}

Solution steps

\frac{d}{d x} (7 x^{- 6} - 5 x^{- 3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x^{- 6}) - \frac{d}{d x} (5 x^{- 3})

\frac{d}{d x} (7 x^{- 6}) = - \frac{42}{x ^{7}}

\frac{d}{d x} (5 x^{- 3}) = - \frac{15}{x ^{4}}

= - \frac{42}{x ^{7}} - (- \frac{15}{x ^{4}})

Simplify

= - \frac{42}{x ^{7}} + \frac{15}{x ^{4}}

\int cot^{7} (x) csc^{2} (x) d x

y = - 10

\frac{d}{d y} (x^{2 y})

36 y^{^{''}} + 36 y^{^{'}} + 11 y = 0, y (0) = 6, y^{^{'}} (0) = 5

What is the derivative of 7x^{-6}-5x^{-3} ?
The derivative of 7x^{-6}-5x^{-3} is -(42)/(x^7)+(15)/(x^4)
What is the first derivative of 7x^{-6}-5x^{-3} ?
The first derivative of 7x^{-6}-5x^{-3} is -(42)/(x^7)+(15)/(x^4)