What is the derivative of-4x^{1/4}+3x^{-6} ?

The derivative of-4x^{1/4}+3x^{-6} is (-x^7-18x^{3/4})/(x^{31/4)}

What is the first derivative of-4x^{1/4}+3x^{-6} ?

The first derivative of-4x^{1/4}+3x^{-6} is (-x^7-18x^{3/4})/(x^{31/4)}

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\frac{d}{d x} (- 4 x^{\frac{1}{4}} + 3 x^{- 6})

\frac{- x ^{7} - 18 x ^{\frac{3}{4}}}{x ^{\frac{31}{4}}}

Solution steps

\frac{d}{d x} (- 4 x^{\frac{1}{4}} + 3 x^{- 6})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (4 x^{\frac{1}{4}}) + \frac{d}{d x} (3 x^{- 6})

\frac{d}{d x} (4 x^{\frac{1}{4}}) = \frac{1}{x ^{\frac{3}{4}}}

\frac{d}{d x} (3 x^{- 6}) = - \frac{18}{x ^{7}}

= - \frac{1}{x ^{\frac{3}{4}}} - \frac{18}{x ^{7}}

Simplify

- \frac{1}{x ^{\frac{3}{4}}} - \frac{18}{x ^{7}} : \frac{- x ^{7} - 18 x ^{\frac{3}{4}}}{x ^{\frac{31}{4}}}

= \frac{- x ^{7} - 18 x ^{\frac{3}{4}}}{x ^{\frac{31}{4}}}

What is the derivative of-4x^{1/4}+3x^{-6} ?
The derivative of-4x^{1/4}+3x^{-6} is (-x^7-18x^{3/4})/(x^{31/4)}
What is the first derivative of-4x^{1/4}+3x^{-6} ?
The first derivative of-4x^{1/4}+3x^{-6} is (-x^7-18x^{3/4})/(x^{31/4)}