Question

tan^-1(8x/1-15x^2) w. r. to x​

Answer 1

Answer:

Let y=tan

−1

(

1−15x

2

8x

)

=tan

−1

[

1−(5x)(3x)

5x+3x

]

=tan

−1

(5x)+tan

−1

(3x)

Differentiating w.r.t. x, we get

dx

dy

=

dx

d

[tan

−1

(5x)+tan

−1

(3x)]

=

dx

d

[tan

−1

(5x)]+

dx

d

[tan

−1

(3x)]

=

1+(5x)

2

1

⋅

dx

d

(5x)+

1+(3x)

2

1

⋅

dx

d

(3x)

=

1+25x

2

1

×5+

1+9x

2

1

×3

=

1+25x

2

5

+

1+9x

2

3