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Question

Find the Derivative of Sin x.


A

sin x

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B

cos x

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C

-cos x

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D

-sin x

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Solution

The correct option is B

cos x


Let f(x)=sin x.

f(x) =limh0=sin(x+h)sin(x)sinxh

we know, sin h0 and cos h1 ash D

=limh0sin x(cosh1)h+sin hcos xh

Clearly(cosh1h)0 as h0 [I hospitals Rules]

andsinhh as h0

=limh0(sinhh)(cosx)=1(cosx)=cosx

Derivative of sinx=cosx


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