RBSE Solutions for Class 12 Maths Chapter 7 Differentiation Ex 7.1

Rajasthan Board RBSE Class 12 Maths Chapter 7 Differentiation Ex 7.1

Find the derivative of following functions w.r.t. x :

Question 1.
sin (x²)
Solution:
Let y = sin (x²)
DifF. w.r.t.x,

Question 2.
tan (2x + 3)
Solution:
Let y = tan (2x + 3)
DifF. w.r.t.x,
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) (tan(2x + 3))
= sec² (2x + 3) \(\frac { d }{ dx } \) (2x + 3)
= sec² (2x + 3).(2 × 1 + 0)
= 2 sec² (2x + 3).

Question 3.
sin {cos (x²)}
Solution:
Let y = sin {cos (x²)}
DifF. w.r.t. x,
\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) sin (cos(x²))
cos (cos x²). (- sin x²) \(\frac { d }{ dx } \) x²
= -cos (cos x²) sin (x²). 2x
= -2x sin (x²) cos (cos x²)

Question 4.

Solution:

Question 5.

Solution:

Question 6.
sin x°
Solution:

Question 7.

Solution:

Question 8.
sec x°
Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.
a tan3x
Solution:

Question 14.
loge (sec x + tan x)
Solution :

Question 15.
sin3 x. sin 3x.
Solution:

= 12 sin³ x . cos x – 24 sin⁵ x cos x
= 12 sin³ x cos x (1 – 2 sin² x)
= 12 sin³ x cos x . cos 2x
= 6 sin² x . 2 sin x . cos x . cos 2x
= 6 sin² x . sin 2x . cos 2x
= 3 sin² x . 2 sin 2x . cos 2x
= 3 sin² x sin 2(2x)
= 3 sin² x . sin 4x.

RBSE Solutions for Class 12 Maths