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

The derivative of f(x)=-2x^4+x^{-2}-3x^{3/4} is (-8x^{1/4}-9x^3-32x^{25/4})/(4x^{13/4)}

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

The first derivative of f(x)=-2x^4+x^{-2}-3x^{3/4} is (-8x^{1/4}-9x^3-32x^{25/4})/(4x^{13/4)}

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derivative of

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

\frac{- 8 x ^{\frac{1}{4}} - 9 x ^{3} - 32 x ^{\frac{25}{4}}}{4 x ^{\frac{13}{4}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (2 x^{4}) = 8 x^{3}

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

\frac{d}{d x} (3 x^{\frac{3}{4}}) = \frac{9}{4 x ^{\frac{1}{4}}}

= - 8 x^{3} - \frac{2}{x ^{3}} - \frac{9}{4 x ^{\frac{1}{4}}}

Simplify

- 8 x^{3} - \frac{2}{x ^{3}} - \frac{9}{4 x ^{\frac{1}{4}}} : \frac{- 8 x ^{\frac{1}{4}} - 9 x ^{3} - 32 x ^{\frac{25}{4}}}{4 x ^{\frac{13}{4}}}

= \frac{- 8 x ^{\frac{1}{4}} - 9 x ^{3} - 32 x ^{\frac{25}{4}}}{4 x ^{\frac{13}{4}}}

cos (π - 7 x)

\int_{0}^{3} x^{\frac{1}{2}} d x

\frac{1}{x ^{\frac{23}{9}}}

\int_{1}^{\infty} x^{- \frac{1}{6}} d x

x \to 8 - lim (\frac{7}{x - 8})

What is the derivative of f(x)=-2x^4+x^{-2}-3x^{3/4} ?
The derivative of f(x)=-2x^4+x^{-2}-3x^{3/4} is (-8x^{1/4}-9x^3-32x^{25/4})/(4x^{13/4)}
What is the first derivative of f(x)=-2x^4+x^{-2}-3x^{3/4} ?
The first derivative of f(x)=-2x^4+x^{-2}-3x^{3/4} is (-8x^{1/4}-9x^3-32x^{25/4})/(4x^{13/4)}