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Differentiate.

$ V(t) = \frac {4 + 1}{te^t} $

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01:12

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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02:37

it's clear. So when you read here, So, yeah, we're gonna fund that derivative in terms of tea. So I wrote it a different way. I wrote it T plus four, and I put e in the numerator. It just becomes equal to D over d t 30 plus four e to the t you to the negative t terms T minus T plus or eat the negative t d over DT of tea. Fall over Tea Square. Then we've simplify this when we got t negative d over DT For tea comes T plus four. Eat the negative T plus one plus zero eat to the negative T minus T plus four e to the negative T crawl over Teeth Square. This becomes equal to t terms e to the negative T minus T plus four. Eat the negative T minus T plus four. Eat the negative T while over he's square, you simplify to get T square plus 14th plus four plus four times E to the negative t well over a T square

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