What is the derivative of 2x^{3/4}+4x^{-1/4} ?

The derivative of 2x^{3/4}+4x^{-1/4} is 3/(2x^{1/4)}-1/(x^{5/4)}

What is the first derivative of 2x^{3/4}+4x^{-1/4} ?

The first derivative of 2x^{3/4}+4x^{-1/4} is 3/(2x^{1/4)}-1/(x^{5/4)}

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

\frac{3}{2 x ^{\frac{1}{4}}} - \frac{1}{x ^{\frac{5}{4}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (4 x^{- \frac{1}{4}}) = - \frac{1}{x ^{\frac{5}{4}}}

= \frac{3}{2 x ^{\frac{1}{4}}} - \frac{1}{x ^{\frac{5}{4}}}

What is the derivative of 2x^{3/4}+4x^{-1/4} ?
The derivative of 2x^{3/4}+4x^{-1/4} is 3/(2x^{1/4)}-1/(x^{5/4)}
What is the first derivative of 2x^{3/4}+4x^{-1/4} ?
The first derivative of 2x^{3/4}+4x^{-1/4} is 3/(2x^{1/4)}-1/(x^{5/4)}