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Popular >

derivative of sqrt(5x)+(sqrt(7)/x)

Solution

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

Solution

\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}

Popular Examples

integral from 1 to 5 of (ln(x))/(x^5)

\int_{1}^{5} \frac{ln ( x )}{x ^{5}} d x

derivative of f(x)=4x^3-11x^2-14x+19 derivative of

f (x) = 4 x^{3} - 11 x^{2} - 14 x + 19

limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))}

x \to 0 lim ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i n ( x )}})

integral from 6 to 8 of (82)/((x-6)^3)

\int_{6}^{8} \frac{82}{( x - 6 ) ^{3}} d x

derivative of (2x-x^2^3)

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

Frequently Asked Questions (FAQ)

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)}