Q7 of 29 Page 1

If ey (x + 1) = 1, show that

Given,


ey (x + 1) = 1


….. [1]


As,


ey (x + 1) = 1


Differentiating both side with respect to ‘x’



Product rule: if f(x) and g(x) are two differentiable functions then


[f(x)g(x)]’ = f(x)g(x)’ + g(x)f(x)’


Now, applying Product rule on LHS and differentiation of any constant value is 0.



Chain rule: Let F = f o g, or equivalently, F(x) = f(g(x)) for all x. then F’(x) = f’(g(x))g’(x)


So



{displaystyle F'(x)=f'(g(x))g'(x).}


{displaystyle F'(x)=f'(g(x))g'(x).}




…. [From 1]


More from this chapter

All 29 →
5

How many equivalence relations on the set {1,2,3} containing (1,2) and (2,1) are there in all? Justify your answer.

 6

Let li, mi and ni; i = 1, 2, 3 be the direction cosines of three mutually perpendicular vectors in space. Show that AA’ = I3, where A =

8

Find the sum of the order and the degree of the following differential equations:


 9

Find the Cartesian and Vector equations of the line which passes through the point (2,4,5) and parallel to the line given by.