What is the derivative of f(x)=x^{3/2}+1/(x^{5/2)} ?

The derivative of f(x)=x^{3/2}+1/(x^{5/2)} is (3x^4-5)/(2x^{7/2)}

What is the first derivative of f(x)=x^{3/2}+1/(x^{5/2)} ?

The first derivative of f(x)=x^{3/2}+1/(x^{5/2)} is (3x^4-5)/(2x^{7/2)}

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derivative of

f (x) = x^{\frac{3}{2}} + \frac{1}{x ^{\frac{5}{2}}}

\frac{3 x ^{4} - 5}{2 x ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (x^{\frac{3}{2}} + \frac{1}{x ^{\frac{5}{2}}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{\frac{3}{2}}) + \frac{d}{d x} (\frac{1}{x ^{\frac{5}{2}}})

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

\frac{d}{d x} (\frac{1}{x ^{\frac{5}{2}}}) = - \frac{5}{2 x ^{\frac{7}{2}}}

= \frac{3 x ^{\frac{1}{2}}}{2} - \frac{5}{2 x ^{\frac{7}{2}}}

Simplify

\frac{3 x ^{\frac{1}{2}}}{2} - \frac{5}{2 x ^{\frac{7}{2}}} : \frac{3 x ^{4} - 5}{2 x ^{\frac{7}{2}}}

= \frac{3 x ^{4} - 5}{2 x ^{\frac{7}{2}}}

What is the derivative of f(x)=x^{3/2}+1/(x^{5/2)} ?
The derivative of f(x)=x^{3/2}+1/(x^{5/2)} is (3x^4-5)/(2x^{7/2)}
What is the first derivative of f(x)=x^{3/2}+1/(x^{5/2)} ?
The first derivative of f(x)=x^{3/2}+1/(x^{5/2)} is (3x^4-5)/(2x^{7/2)}