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

In this problem, we're asked to find the derivative d dt of negative 5 x. Now, this is a sort of tricky one that's meant to trip you up a little bit here because we're asked to differentiate with respect to t. That's what d dt means. But there's no t in this function, negative 5 x. So what does that mean for us? Well, since we're differentiating with respect to t and there is no t anywhere in this function, all of this is effectively a constant. Now I know that x, the way that we think of it is not a constant. It's a variable. But when we're thinking about this as a function of t, since there is no t here, this is effectively all a constant. Meaning that if we're taking the derivative of a constant, then our answer is just 0. We know that the derivative of any constant, no matter what that constant is, is always going to be 0. Since the variable that we're differentiating with respect to t is nowhere to be found, All of this is just a constant, and the answer here for a derivative is just 0. Feel free to let me know if you have any questions here.

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.
$d/dt(-5x)$

$0$

$x$

$t$

$-5$

Verified step by step guidance

Identify the function to differentiate: The given function is -5x, where x is treated as a constant with respect to t.

Recall the rule for differentiating constants: The derivative of a constant multiplied by a variable is the constant itself multiplied by the derivative of the variable.

Since x is treated as a constant with respect to t, its derivative with respect to t is 0. Therefore, the derivative of -5x with respect to t is -5 multiplied by 0.

Simplify the expression: -5 * 0 results in 0.

Conclude that the derivative of -5x with respect to t is 0.