Question

differentiate sin4xcos 3x e^2x​

Answer 1

Answer:

e^2x ( sinx + 1/2cosx + sin7x + 7/2cos7x )

Step-by-step explanation:

d(sin4x × cos3x × e^2x)/xx=

= (cos3x × e^2x × 4cos4x) + (sin4x × e^2x × (-3sin3x)) +

(sin4x × cos3x × 2e^2x)

= e^2x × (4cos3xcos4x+2sin4xcos3x-3sin4xsin3x)

= e^2x × (4 × 1/2(cos7x+cosx) + 2 × 1/2(sin7x+sinx) -

3 × 1/2(cosx-cos7x))

= e^2x × (2cos7x+2cosx+sin7x+sinx-3/2cosx+3/2cos7x)

= e^2x × (sin7x+sinx+7/2cos7x+1/2cosx)