## 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 (x^{2})

Solution:

Let y = sin (x^{2})

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))

= sec^{2} (2x + 3) \(\frac { d }{ dx } \) (2x + 3)

= sec^{2} (2x + 3).(2 × 1 + 0)

= 2 sec^{2} (2x + 3).

Question 3.

sin {cos (x^{2})}

Solution:

Let y = sin {cos (x^{2})}

DifF. w.r.t. x,

\(\frac { dy }{ dx } \) = \(\frac { d }{ dx } \) sin (cos(x^{2}))

cos (cos x^{2}). (- sin x^{2}) \(\frac { d }{ dx } \) x^{2}

= -cos (cos x^{2}) sin (x^{2}). 2x

= -2x sin (x^{2}) cos (cos x^{2})

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 sin^{3} x . cos x – 24 sin^{5} x cos x

= 12 sin^{3} x cos x (1 – 2 sin^{2} x)

= 12 sin^{3} x cos x . cos 2x

= 6 sin^{2} x . 2 sin x . cos x . cos 2x

= 6 sin^{2} x . sin 2x . cos 2x

= 3 sin^{2} x . 2 sin 2x . cos 2x

= 3 sin^{2} x sin 2(2x)

= 3 sin^{2} x . sin 4x.

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