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Differentiate the function.$ D(t) = \frac {1 + 16t^2}{(4t)^3} $

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01:14

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

University of Nottingham

Idaho State University

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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Differentiate the function…

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Differentiate.

$ y…

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differentiate the function…

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it's clear. So when you right here. So we have d of T, which can be re written into one over 64 t to the negative three plus one over four t to the negative one. Used to some indifference rule. We get d over Deep T won over 64 tete the negative three plus de over DT 1/4 t to the negative one. We used the constant multiple roll and we take out the Constance when we apply the pa rolled to get won over 64 Negative. Three t to the negative. Three minus one. Power close 1/4 Negative one t to the negative one minus one Power and we get negative. Three over a 64 t to the fourth power minus one over four T square.

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