derivative of (90/x) — step-by-step solution

To ease differentiation, the expression

\frac{90}{x}

is turned into

90 x^{-1}

Let's perform the differentiation:

\frac{d}{d x} (90 x^{-1})

We differentiate using:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{n - 1}

(where f =

x

)

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

\frac{d}{d x} (90 x^{-1})

90 \cdot \frac{d}{d x} (x^{-1})

■The derivative of x^n is n*x^(n-1):

\frac{d}{d x} (x^{-1})

-1 \cdot x^{-2}

90 \cdot (-1 \cdot x^{-2})

ⓘ A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

90 \cdot (-1)

-90

-90 x^{-2}

ⓘ The factor is moved to the numerator or the denominator by changing the sign of its exponent, for a nonzero base:

- 90 x^{-2}

- \frac{90}{x^{2}}

▶Derivative:

- \frac{90}{x^{2}}