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Question

Differentiate secx by the first principle.


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Solution

Let us consider

secx=1cosx

By quotient rule derivative of secx=1cosx

[The quotient rule of differentiation is defined as the ratio of two functions (1st function / 2nd function ), is equal to the ratio of (differentiation of 1st function ×the 2nd function - differentiation of the second function ×the first function ) to the square of the 2nd function]

so,

ddx×1-ddxcosx×1(cosx)2

by simplifying the equation

=0×cosx-ddxcosx×1(cosx)2=sinxcosx×cosx=sinxcosx×1cosx=tanx×secx

Thus, differentiation of secx by the first principle istanx×secx.


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