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

The derivative of 2x^{1/2}+2x^{-4}-1 is (x^5-8x^{1/2})/(x^{11/2)}

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

The first derivative of 2x^{1/2}+2x^{-4}-1 is (x^5-8x^{1/2})/(x^{11/2)}

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

\frac{x ^{5} - 8 x ^{\frac{1}{2}}}{x ^{\frac{11}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (2 x^{- 4}) = - \frac{8}{x ^{5}}

\frac{d}{d x} (1) = 0

= \frac{1}{x ^{\frac{1}{2}}} - \frac{8}{x ^{5}} - 0

Simplify

\frac{1}{x ^{\frac{1}{2}}} - \frac{8}{x ^{5}} - 0 : \frac{x ^{5} - 8 x ^{\frac{1}{2}}}{x ^{\frac{11}{2}}}

= \frac{x ^{5} - 8 x ^{\frac{1}{2}}}{x ^{\frac{11}{2}}}

What is the derivative of 2x^{1/2}+2x^{-4}-1 ?
The derivative of 2x^{1/2}+2x^{-4}-1 is (x^5-8x^{1/2})/(x^{11/2)}
What is the first derivative of 2x^{1/2}+2x^{-4}-1 ?
The first derivative of 2x^{1/2}+2x^{-4}-1 is (x^5-8x^{1/2})/(x^{11/2)}