What is the derivative of f(x)= 4/(x^4)+10sqrt(x) ?

The derivative of f(x)= 4/(x^4)+10sqrt(x) is (-16+5x^{9/2})/(x^{9/2)sqrt(x)}

What is the first derivative of f(x)= 4/(x^4)+10sqrt(x) ?

The first derivative of f(x)= 4/(x^4)+10sqrt(x) is (-16+5x^{9/2})/(x^{9/2)sqrt(x)}

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derivative of

f (x) = \frac{4}{x ^{4}} + 10 x

\frac{- 16 + 5 x ^{\frac{9}{2}}}{x ^{\frac{9}{2}} x}

Solution steps

\frac{d}{d x} (\frac{4}{x ^{4}} + 10 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{4}{x ^{4}}) + \frac{d}{d x} (10 x)

\frac{d}{d x} (\frac{4}{x ^{4}}) = - \frac{16}{x ^{5}}

\frac{d}{d x} (10 x) = \frac{5}{x}

= - \frac{16}{x ^{5}} + \frac{5}{x}

Simplify

- \frac{16}{x ^{5}} + \frac{5}{x} : \frac{- 16 + 5 x ^{\frac{9}{2}}}{x ^{\frac{9}{2}} x}

= \frac{- 16 + 5 x ^{\frac{9}{2}}}{x ^{\frac{9}{2}} x}

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What is the derivative of f(x)= 4/(x^4)+10sqrt(x) ?
The derivative of f(x)= 4/(x^4)+10sqrt(x) is (-16+5x^{9/2})/(x^{9/2)sqrt(x)}
What is the first derivative of f(x)= 4/(x^4)+10sqrt(x) ?
The first derivative of f(x)= 4/(x^4)+10sqrt(x) is (-16+5x^{9/2})/(x^{9/2)sqrt(x)}