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The partial derevator?

Partial derivatives are defined as derivatives of a function of multiple variables when all except the variable of interest are held fixed during the differentiation. Suppose that you have a function f(x,y) of two variables. When you fix one variable then you got a plane whose intersection with your surface z=f(x,y) gives a curve in which one variable is constant and the other varies and finally you can find the slope of the tangent line at that curve and we call it the partial derivative of the function f(x,y) with respect to the variable which varies.

w = ( 4 x − 3y + 2z)5

First partially differentiate w.r.t x by using the power rule

=5.( 4 x − 3y + 2z)4 (4-0+0)

=20 ( 4 x − 3y + 2z)4 

now again partially differentiate the function 20 ( 4 x − 3y + 2z)4 w.r.t "y" by using the power rule 

        =20.4 ( 4 x − 3y + 2z)4 (0-3+0)

      = - 240. ( 4 x − 3y + 2z)3

now again partially differentiate the function  -240. ( 4 x − 3y + 2z)3 w.r.t "z" by using the power rule          

= - 240. 3( 4 x − 3y + 2z)2 .(0+0+2)

= - 1440( 4 x − 3y + 2z)2 

.explain the formula for finding projection of A on B and projection of B on A? 

Suppose that you have two vectors namely "a" and "b" and you draw them so that they start from the same point and if you are not given the vectors in this form then note that you can redraw the given vectors such that they start from the same point say "O". Now you can draw two rectangular components of any vector with respect to the other, by dropping a perpendicular from the head of one vector ("a" say) to the other ("b").

One component of the vector "a" will be along the other vector which is "b" and one component will be perpendicular to that component. Now the component of the vector "a" along the vector "b" is known as the projection of the first vector "a" along the vector "b". And if we are given the angle between these two vectors say
( )then you can calculate this projection by using right angle triangle and the projection of "a "on "b" will be "




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