What is the derivative of ((x+30sqrt(x^2+100))/x) ?

The derivative of ((x+30sqrt(x^2+100))/x) is (x^3-3000)/(x^2sqrt(x^2+100))

What is the first derivative of ((x+30sqrt(x^2+100))/x) ?

The first derivative of ((x+30sqrt(x^2+100))/x) is (x^3-3000)/(x^2sqrt(x^2+100))

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\frac{d}{d x} (\frac{( x + 30 ) x ^{2} + 100}{x})

\frac{x ^{3} - 3000}{x ^{2} x ^{2} + 100}

Solution steps

\frac{d}{d x} (\frac{( x + 30 ) x ^{2} + 100}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ( x + 30 ) x ^{2} + 100 ) x - \frac{d x}{d x} ( x + 30 ) x ^{2} + 100}{x ^{2}}

\frac{d}{d x} ((x + 30) x^{2} + 100) = \frac{2 x ^{2} + 30 x + 100}{x ^{2} + 100}

\frac{d x}{d x} = 1

= \frac{\frac{2 x ^{2} + 30 x + 100}{x ^{2} + 100} x - 1 \cdot ( x + 30 ) x ^{2} + 100}{x ^{2}}

Simplify

\frac{\frac{2 x ^{2} + 30 x + 100}{x ^{2} + 100} x - 1 \cdot ( x + 30 ) x ^{2} + 100}{x ^{2}} : \frac{x ^{3} - 3000}{x ^{2} x ^{2} + 100}

= \frac{x ^{3} - 3000}{x ^{2} x ^{2} + 100}

f (x) = 9 + 4 x

\int x^{5} + 8 x^{3} - 9 x^{2} + 7 x - 5 d x

\int - x^{3} + \frac{1}{x ^{2}} d x

\int \frac{4 e ^{- \frac{3}{x ^{5}}}}{x ^{6}} d x

\frac{\partial}{\partial y} ((x + y) e^{y^{2}})

What is the derivative of ((x+30sqrt(x^2+100))/x) ?
The derivative of ((x+30sqrt(x^2+100))/x) is (x^3-3000)/(x^2sqrt(x^2+100))
What is the first derivative of ((x+30sqrt(x^2+100))/x) ?
The first derivative of ((x+30sqrt(x^2+100))/x) is (x^3-3000)/(x^2sqrt(x^2+100))