What is the derivative of sqrt(5x)+(sqrt(7)/x) ?

The derivative of sqrt(5x)+(sqrt(7)/x) is (sqrt(5)x^{3/2}-2sqrt(7))/(2x^{3/2)sqrt(x)}

What is the first derivative of sqrt(5x)+(sqrt(7)/x) ?

The first derivative of sqrt(5x)+(sqrt(7)/x) is (sqrt(5)x^{3/2}-2sqrt(7))/(2x^{3/2)sqrt(x)}

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\frac{d}{d x} (5 x + \frac{7}{x})

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

Solution steps

\frac{d}{d x} (5 x + \frac{7}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x) + \frac{d}{d x} (\frac{7}{x})

\frac{d}{d x} (5 x) = \frac{5}{2 x}

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

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

Simplify

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

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

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