Provide an Appropriate Response $\mathbf { u }$ Is a Differentiable Function Of

question 95

Essay

Provide an appropriate response.
-Prove that if $\mathbf { u }$ is a differentiable function of $\mathrm { t }$ and $\mathrm { f }$ is a differentiable scalar function of $\mathrm { t }$ , then
$\frac { d } { d t } ( f u ) = \frac { d f } { d t } \mathbf { u } + f \frac { d u } { d t } \text {. }$

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Definitions:

Exponential Equation

An equation where the variable appears in the exponent, expressing the relationship between two quantities where one varies as a constant power of another.

Decimal Places

The count of numbers present after the decimal point in a decimal numeral.

Annual Interest Rate

The percentage of principal charged by lenders or paid to investors per annum.

Compounded Continuously

A calculation involving the natural exponential function for the interest that is added to an amount of money based on an infinitely small rate over a period of time.