derivative of (7x^2/(x^3)) — step-by-step solution

1) Let's perform the differentiation:

\frac{d}{d x} (\frac{7 x^{2}}{x^{3}})

ⓘ The original denominator must remain nonzero. The fraction is simplified by dividing the numerator and the denominator by their common factor:

\frac{7 x^{2}}{x^{3}}

\frac{7}{x}

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

We differentiate

p1

7

and

q2

x

using:

\frac{d}{d x} (\frac{p1}{q2}) = \frac{\frac{d}{d x} (p1) \cdot q2 - p1 \cdot \frac{d}{d x} (q2)}{{q2}^{2}}

2) Let's perform the differentiation

p1

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

ⓘ The derivative of a constant is zero:

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

0

0

3) Let's perform the differentiation

q2

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

ⓘ The derivative of x is 1:

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

1

1

4) Let's evaluate the resulting derivative (

\frac{p1}{q2}

)':

\frac{0 \cdot x - 7 \cdot 1}{x^{2}}

ⓘ A product with a zero factor is zero:

0 \cdot x

0

\frac{0 - 7}{x^{2}}

ⓘ Adding 0 changes nothing:

0 - 7

-7

- \frac{7}{x^{2}}

5) You can then resume the derivation:

ⅰ

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

- \frac{7}{x^{2}}

▶Derivative:

- \frac{7}{x^{2}}