Question

Differentiate

x cos
x

using first principle.​

Answer 1

Answer:

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Answer 2

Answer:

ANSWER

f

′

(x)=

h→0

lim

h

f(x+h)−f(x)

=

h→0

lim

h

cos(x+h)−cosx

=

h→0

lim

[

h

cosxcosh−sinxsinh−cosx

]

=

h→0

lim

[

h

−cosx(1−cosh)−sinxsinh

]

=

h→0

lim

[

h

−cosx(1−cosh)

=

h

sinxsinh

]

=−cosx(

h→0

lim

h

1−cosh

)−sinx

h→0

lim

(

h

sinh

)

=−cosx.(0)−sinx(1)=−sinx