Question

derivative w.r.t x of (Sin4x)^2​

Answer 1

ANSWER:

Derivative of (sin 4x)² = 4 sin 8x

GIVEN:

(sin 4x)²

TO FIND:

Derivative of (sin 4x)²

FORMULAE:

d/dx (sin x) = cos x

d/dx$( x^n) = nx^{n-1}$

d/dx ax = a

Sin 2x = 2 sin x cos x

EXPLANATION:

= d/dx [(sin 4x)²]

= 2 sin 4x × d/dx (sin 4x)

= 2 sin 4x × (cos 4x) × d/dx (4x)

= 2 sin 4x × (cos 4x) × 4

= 8 sin 4x cos 4x

= 4 (2 sin 4x cos 4x)

= 4 sin 8x

Derivative of (sin 4x)² = 4 sin 8x

Answer 2

Derivative of (sin 4x)² = 4 sin 8x

GIVEN:

(sin 4x)²

TO FIND:

Derivative of (sin 4x)²

FORMULAE:

d/dx (sin x) = cos x

d/dx

d/dx ax = a

Sin 2x = 2 sin x cos x

EXPLANATION:

= d/dx [(sin 4x)²]

= 2 sin 4x × d/dx (sin 4x)

= 2 sin 4x × (cos 4x) × d/dx (4x)

= 2 sin 4x × (cos 4x) × 4

= 8 sin 4x cos 4x

= 4 (2 sin 4x cos 4x)

= 4 sin 8x

Derivative of (sin 4x)² = 4 sin 8x