Q22 of 147 Page 191

If , prove that

Let y =

Differentiation of determinant is given by

∴

Since, a, b, c and l, m, n are constants so, their differentiation is zero.

Also in a determinant if all the elements of row or column turns to be zero then the value of determinant is zero.

∴

Hence, proved.

Using mathematical induction prove that for all positive integers n.

Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.