Find the derivative of the function, ` y=sin 4x cos 5x`.

Find the derivative of the function, ` y=sin 4x cos 5x`.

Find the derivative of the function, ` y=sin 4x cos 5x`.

Find the derivative of the function, ` y=sin 4x cos 5x`.
`y=sin 4x cos 5x`To determine y’, apply the product formula of derivatives which is `(u*v)’=uv’ + vu’` .So let,`u = sin 4x`                        and                       `v= cos 5x`Then, determine the derivative of u and v.`u’ = cos 4x *(4x)’ `                                        `v’=-sin5x *(5x)’“u’= cos 4x * 4`                                              `v’= -sin 5x * 5“u’=4cos 4x `                                                `v’=-5sin 5x`Substitute u, v, u’ and v’ to the formula.`y’ = (sin4xcos5x)’ = sin4x*(-5sin5x) + cos5x*(4cos4x)“y’ = -5sin4xsin5x + 4cos4xcos5x“y’ = 4cos4xcos5x – 5sin4xsin5x`Hence the derivative of the function `y=sin4xcos5x` is `y’=4cos4xcos5x – 5sin4xsin5x` .