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Find equations of the tangent line and normal line to the given curve at the specified point.
$ y = 2xe^x, (0,0) $
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Calculus 1 / AB
The Product and Quotient Rules
Missouri State University
Oregon State University
Harvey Mudd College
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.
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.
Find equations of the tang…
Find equations for the lin…
it's Clarissa when you right here. So we have acts is equal to two x e to the X To find the derivative, we got D over DX. To exceeds the X, we used the product Rule two x d to the axe eat the X plus eat the X d over DX for two X this becomes equal to eat. The axe comes to X plus two and the slope of detention at 00 becomes too. So the equation of attention is why equals two X? We have to note that while we multiply perpendicular lines, there slope is negative one. So the normal normal line has a slope of negative 1/2. So the equation of the normal line is gonna be Y minus zero over X minus zero, which is equal to negative one tough ex. So this becomes a Y is equal to negative 1/2 X for the normal line.
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