1.

12. Find the derivative of (from first principle)sin 4x​

Answer»

Answer:

Given: f(x)=sin4x

To find : DERIVATIVE of f(x)=sin4x from 1st principle

Step-by-step explanation:

f(x)=sin4x

f'(x) = 4Cos4x

using 1st principle

f'(x) = LIM h→ 0 ( f(x + h) - f(x) )/h

= Lim h→ 0 (sin(4x + 4h) - Sin(4x)) /h

Using SinA - SinB = 2Cos((A + B)/2) Sin((A - B)/2)

= Lim h→ 0 2Cos(4x + 2h)Sin(2h) / h

= Lim h→ 0 2Cos(4x + 2h) 2 Sin(2h) / 2h

= Lim h→ 0 4Cos(4x + 2h) Sin(2h) / 2h

using Lim h→ 0 Sin(2h) / 2h = 1

= Lim h→ 0 4Cos(4x + 2h)

= 4Cos4x

f'(x) = 4Cos4x


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