derivative of (4x/(7x-2)) — step-by-step solution

Let's differentiate:

\frac{d}{d x} (\frac{4 x}{7 x - 2})

We differentiate

u1

4 x

and

v2

7 x - 2

using:

\frac{d}{d x} (\frac{u1}{v2}) = \frac{\frac{d}{d x} (u1) \cdot v2 - u1 \cdot \frac{d}{d x} (v2)}{{v2}^{2}}

Let's differentiate

u1

\frac{d}{d x} (4 x)

4

Let's perform the differentiation

v2

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

\frac{d}{d x} (7 x) + 0

7

You can evaluate the resulted derivative (

\frac{u1}{v2}

)':

\frac{4 \cdot (7 x - 2) - 4 x \cdot 7}{{(7 x - 2)}^{2}}

\frac{4 \cdot (7 x - 2) - 28 x}{{(7 x - 2)}^{2}}

\frac{(28 x - 8) - 28 x}{{(7 x - 2)}^{2}}

\frac{0 - 8}{{(7 x - 2)}^{2}}

▶Derivative:

- \frac{8}{{(7 x - 2)}^{2}}