Question

differentiate with respect to x ​

Answer 1

Answer:

Read this as follows: the derivative of y with respect to x is the derivative of the f term multiplied by the g term, plus the derivative of the g term multiplied by the f term. To apply it to the above problem, note that f(x) = (x - 3) and g(x) = (2x2 - 1); f'(x) = 1 and g'(x) = 4x.

Answer 2

Answer:

dx

d

[2

cot(x

2

)

]

=2.

2

cot(x

2

)

1

×

dx

d

[cot(x

2

)]

=

cos(x

2

)

sin(x

2

)

×−cosec

2

(x

2

)×

dx

d

(x

2

)

=

cos(x

2

)

sin(x

2

)

×−

sin

2

(x

2

)

1

×(2x)

=

cosx

2

sinx

2

sinx

2

−2x

=

2sinx

2

cosx

2

sinx

2

−2

2

x

=

sinx

2

sin(2x

2

)