# Question #b7bb9

Jun 6, 2017

#### Explanation:

The $\frac{d}{\mathrm{dx}}$ of the original function is 2x, using the power rule $n {x}^{n - 1}$ where n is our exponent. The derivative of -2 is zero the $\frac{d}{\mathrm{dx}}$ of a constant is always zero. Now we evaluate the $\frac{d}{\mathrm{dx}}$ at 10, so 2(10) = 20.

Jun 6, 2017

Answer: $20$

#### Explanation:

Find derivative of $f \left(x\right) = {x}^{2} - 2$ at $x = 10$

First we need to find the derivative of $f \left(x\right)$ by using the exponent rule which states that $\frac{d}{\mathrm{dx}} {x}^{n} = n {x}^{n - 1}$ and the constant rule which states that $\frac{d}{\mathrm{dx}} c = 0$ for constant $c$. So:
$f ' \left(x\right) = 2 x$

Now to find $f ' \left(10\right)$ we plug $x = 10$ into the derivative function:
$f ' \left(10\right) = 2 \cdot 10 = 20$

Therefore the derivative of $f \left(x\right) = {x}^{2} - 2$ at $x = 10$ is $20$.