Find the indicated derivative. d / d t ( − 5 t ) d/dt(-5t) d / d t ( − 5 t )

In this problem, we're asked to find the derivative d d t of negative five t. Now this d d t just means that we're differentiating with respect to the variable t, the same way that d d x means that we're differentiating with respect to the variable x. So we're gonna treat this the same way we would any derivative. Here, we're taking the derivative of negative 5, a constant, times t. Now I know that when faced with a derivative like this, I can pull my constant out to the front. So this is really negative 5 times the derivative d d t of t. Now using what we know, d d t of t is just going to be 1, so this becomes negative 5 times 1 or just a negative 5. So that's my final derivative here. Now, again, as you get further and further on in taking derivatives, you can recognize almost immediately that ddt of negative 5 t is just negative 5 without having to set up these additional rules. Now if you already recognize that here, great job. Let's keep getting some more practice. Thanks for watching.

3. Techniques of Differentiation

Basic Rules of Differentiation

Business Calculus

3. Techniques of Differentiation

Basic Rules of Differentiation

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Multiple Choice

Find the indicated derivative.
$d/dt(-5t)$

$0$

$-5$

$5$

$5+t$

Verified step by step guidance

Identify the function to differentiate: The given function is $-5t$, where $t$ is the variable.

Recall the power rule for differentiation: $\frac{d}{dt}[t^n] = n \cdot t^{n-1}$. For a constant multiplied by a variable, the constant remains, and the power rule is applied to the variable.

Apply the power rule to $-5t$: Rewrite $-5t$ as $-5 \cdot t^1$. Differentiating this gives $-5 \cdot 1 \cdot t^{1-1}$.

Simplify the expression: $-5 \cdot 1 \cdot t^{1-1}$ simplifies to $-5 \cdot t^0$. Since $t^0 = 1$, the result becomes $-5$.

Conclude that the derivative of $-5t$ with respect to $t$ is $-5$.