What is the derivative of (100(x+25)/x) ?

The derivative of (100(x+25)/x) is -(2500)/(x^2)

What is the first derivative of (100(x+25)/x) ?

The first derivative of (100(x+25)/x) is -(2500)/(x^2)

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\frac{d}{d x} (\frac{100 ( x + 25 )}{x})

- \frac{2500}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{100 ( x + 25 )}{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 100 \frac{d}{d x} (\frac{x + 25}{x})

Apply the Quotient Rule:

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

= 100 \cdot \frac{\frac{d}{d x} ( x + 25 ) x - \frac{d x}{d x} ( x + 25 )}{x ^{2}}

\frac{d}{d x} (x + 25) = 1

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

= 100 \cdot \frac{1 \cdot x - 1 \cdot ( x + 25 )}{x ^{2}}

Simplify

100 \cdot \frac{1 \cdot x - 1 \cdot ( x + 25 )}{x ^{2}} : - \frac{2500}{x ^{2}}

= - \frac{2500}{x ^{2}}

\int \frac{6 x - 12}{x ^{2}} d x

\frac{50000}{s ^{2}}

\int_{0}^{1} \frac{x ^{2}}{x + 1} d x

x y^{2} d x = d y - x d x, y (0) = - 1

\frac{d x}{d y}

What is the derivative of (100(x+25)/x) ?
The derivative of (100(x+25)/x) is -(2500)/(x^2)
What is the first derivative of (100(x+25)/x) ?
The first derivative of (100(x+25)/x) is -(2500)/(x^2)