Using implicit differentiation to find a second derivative
Find
if
In
[link] , we showed that
We can take the derivative of both sides of this equation to find
At this point we have found an expression for
If we choose, we can simplify the expression further by recalling that
and making this substitution in the numerator to obtain
Now that we have seen the technique of implicit differentiation, we can apply it to the problem of finding equations of tangent lines to curves described by equations.
Finding a tangent line to a circle
Find the equation of the line tangent to the curve
at the point
Although we could find this equation without using implicit differentiation, using that method makes it much easier. In
[link] , we found
The slope of the tangent line is found by substituting
into this expression. Consequently, the slope of the tangent line is
Using the point
and the slope
in the point-slope equation of the line, we obtain the equation
(
[link] ).
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,