derivative of sqrt(14x) — step-by-step solution

Let's differentiate:

\frac{d}{d x} (\sqrt{14 x})

We differentiate using:

\frac{d}{d x} (\sqrt{f}) = \frac{d}{d x} (f) \cdot \frac{1}{2 \sqrt{f}}

(where f =

14 x

)

ⓘ The derivative of sqrt(x) is 1/(2*sqrt(x)):

\frac{d}{d x} (\sqrt{14 x})

\frac{d}{d x} (14 x) \cdot \frac{1}{2 \cdot \sqrt{14 x}}

\frac{d}{d x} (14 x) \cdot \frac{1}{2 \cdot \sqrt{14 x}}

ⓘ Multiplying a fraction by a term multiplies its numerator:

\frac{d}{d x} (14 x) \cdot \frac{1}{2 \cdot \sqrt{14 x}}

\frac{\frac{d}{d x} (14 x) \cdot 1}{2 \cdot \sqrt{14 x}}

\frac{\frac{d}{d x} (14 x)}{2 \cdot \sqrt{14 x}}

■A constant factor stays in front of the derivative, (k*u)' = k*u':

\frac{d}{d x} (14 x)

14

\frac{14}{2 \cdot \sqrt{14 x}}

ⓘ A fraction is simplified by dividing the numerator and the denominator by the same number:

\frac{14}{2 \cdot \sqrt{14 x}}

\frac{7}{\sqrt{14 x}}

▶Derivative:

\frac{7}{\sqrt{14 x}}