What is the derivative of f(x)=sqrt(x)+1/(sqrt(x^3)) ?

The derivative of f(x)=sqrt(x)+1/(sqrt(x^3)) is 1/(2sqrt(x))-(3x^2)/(2(x^3)^{3/2)}

What is the first derivative of f(x)=sqrt(x)+1/(sqrt(x^3)) ?

The first derivative of f(x)=sqrt(x)+1/(sqrt(x^3)) is 1/(2sqrt(x))-(3x^2)/(2(x^3)^{3/2)}

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derivative of

f (x) = x + \frac{1}{x ^{3}}

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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