Question

differentiate the function w. r. t x e^x / 1+x^2​

Answer 1

Let y=

(x−3)(x−4)(x−5)

(x−1)(x−2)

Taking logarithm on both the sides, we obtain

logy=log

(x−3)(x−4)(x−5)

(x−1)(x−2)

⇒logy=

2

1

log[

(x−3)(x−4)(x−5)

(x−1)(x−2)

]

⇒logy=

2

1

[log[(x−1)(x−2)]−log[(x−3)(x−4)(x−5)]]

⇒logy=

2

1

[log(x−1)+log(x−2)−log(x−3)−log(x−4)−log(x−5)]

Differentiating both sides with respect to x, we obtain

⇒

y

1

dx

dy

=

2

1

[

x−1

1

.+

x−2

1

−

x−3

1

−

x−4

1

−

x−5

1

]

⇒

dx

dy

=

2

y

(

x−1

1

+

x−2

1

−

x−3

1

−

x−4

1

−

x−5

1

)

∴

dx

dy

=

2

1

(x−3)(x−4)(x−5)

(x−1)(x−2)

[

x−1

1

+

x−2

1

−

x−3

1

−

x−4

1

−

x−5

1

]