Question

hyyy everyone...!!!

plzz solve part iv v nd vi...


it's urgent.. class 12th differentiation maths..
thanks​

Answer 1

★★Heya★★

Before solving these question let's discuss a very basic rule ( Chain rule of Differentiation ) .

IF the function is like this F(g(x) then it's Differentiation is done by using chain rule of Differentiation i,e

it's Differentiation is

F'(g(x) × g'(x)

Q.1:-

F( x ) = Sin ( Cos x² )

F'( x ) = Cos ( Cos x² ) × -Sin ( x² ) × 2x

F' (x ) = -2x Cos ( Cos x² ) × Sin ( x² )

Q.2

F( x ) = Cos ( aCos x + b Sin x )

F' ( x ) = -Sin ( aCos x + b Sin x ) ×

( - a Sin x + b Cos x )

Q.3

$f(x) = \sqrt{ \sin( \sqrt{1 - x {}^{2} } ) } \\ \\ f {}^{1} (x) = (1 \div 2 ) \sqrt{ \sin( \sqrt{1 - x {}^{2} } ) } \times \cos( \sqrt{1 - x {}^{2} } ) \times (1 \div 2 \sqrt{1 - x {}^{2} } ) \times - 2x$