Second Order Derivative

Given,

%5Cfrac%7Bd%7D%7Bd%20x%7D%5Cleft(e%5E%7Ba%20x%7D%20%5Ccos%20b%20x%5Cright)%3Dr%20e%5E%7Ba%20x%7D%20%5Ccos%20(b%20x%2B%5Calpha)

, then

r%3D%3F

Let

y%3De%5E%7Ba%20x%7D%20%5Ccdot%20%5Ccos%20b%20x

Let

y%3De%5E%7Ba%20x%7D%20%5Ccdot%20%5Ccos%20b%20x

%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%3Da%20e%5E%7Ba%20x%7D%20%5Ccdot%20%5Ccos%20b%20x-b%20e%5E%7Ba%20x%7D%20%5Ccdot%20%5Csin%20b%20x

%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%3De%5E%7Ba%20x%7D(a%20%5Ccos%20b%20x-b%20%5Csin%20b%20x)

a%3Dr%20%5Ccos%20%5Calpha%20%3Cbr%20%2F%3Eb%3Dr%20%5Csin%20%5Calpha%5C%7D

...(i)
Then,

%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%20%3De%5E%7Ba%20x%7D%20%5Ccdot%20r%5C%7B%5Ccos%20b%20x%20%5Ccdot%20%5Ccos%20%5Calpha-%5Csin%20b%20x%20%5Ccdot%20%5Csin%20%5Calpha%5C%7D

%5Cfrac%7Bd%20y%7D%7Bd%20x%7D%3De%5E%7Ba%20x%7D%20%5Ccdot%20r%20%5Ccos%20(b%20x%2B%5Calpha)

...(ii)
Where,

%5Ctan%20%5Calpha%3D%5Cfrac%7Bb%7D%7Ba%7D%20%5CRightarrow%20%5Calpha%3D%5Ctan%20%5E%7B-1%7D%5Cleft(%5Cfrac%7Bb%7D%7Ba%7D%5Cright)

and

r%5E%7B2%7D%5Cleft(%5Ccos%20%5E%7B2%7D%20%5Calpha%2B%5Csin%20%5E%7B2%7D%20%5Calpha%5Cright)%3Da%5E%7B2%7D%2Bb%5E%7B2%7D

r%5E%7B2%7D%3Da%5E%7B2%7D%2Bb%5E%7B2%7D

r%3D%5Csqrt%7Ba%5E%7B2%7D%2Bb%5E%7B2%7D%7D

Chapter Questions
1 MCQs