# Question #d54f6

Aug 29, 2015

See explanation

#### Explanation:

I'll make two guesses at what the intended question is.

Guess 1
Assume that $x$ is a function of $t$ and find the derivative with respest to $t$ of the expression $4 {x}^{2} + 55446$

Find $\frac{d}{\mathrm{dt}} \left(4 {x}^{2} + 55446\right)$

We'll use implicit differentiation (which means we're using the chain rule.

The derivative of the constant $55446$ is $0$, so we have:

$\frac{d}{\mathrm{dt}} \left(4 {x}^{2} + 55446\right) = 8 x \frac{\mathrm{dx}}{\mathrm{dt}}$

Guess 2

Assume that the intended question is

Find $\frac{\mathrm{dx}}{\mathrm{dt}}$ if $4 {x}^{2} = 55446$

In this case we get: $8 x \frac{\mathrm{dx}}{\mathrm{dt}} = 0$,

so $\frac{\mathrm{dx}}{\mathrm{dt}} = \frac{1}{8 x}$