Respuesta :
y = x⁵ sin(2x ) cos(4x)
y' = d/dx (x⁵ sin (2x) × cos (4x) + x⁵ sin(2x) ). ×
d/dx (cos(4x) )
y' = 5x⁴ sin(2x) cos(4x)+2x⁵ cos(2x) cos(4x) -4x⁵ sin(2x) sin(4x)
y' = d/dx (x⁵ sin (2x) × cos (4x) + x⁵ sin(2x) ). ×
d/dx (cos(4x) )
y' = 5x⁴ sin(2x) cos(4x)+2x⁵ cos(2x) cos(4x) -4x⁵ sin(2x) sin(4x)
The derivative of the equation will be y' = 5y/x + 2y cot (2x) - 4y tan (4x).
What is differential equation?
An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations.
The derivatives might be of any order, some terms might contain product of derivatives and the variable itself, or with derivatives themselves.
They can also be for multiple variables.
y = x⁵ sin(2x ) cos(4x)
The differentiation;
y' = d/dx (x⁵ sin (2x) × cos (4x) + x⁵ sin(2x) ). × d/dx (cos(4x) )
y' = 5x⁴ sin(2x) cos(4x)+2x⁵ cos(2x) cos(4x) -4x⁵ sin(2x) sin(4x)
From the given equation;
y' = 5y/x + 2x⁵ cos(2x) cos(4x) - 4x⁵ sin(2x) sin(4x)
y' = 5y/x + 2y cot (2x) - 4y tan (4x)
Learn more about derivatives ;
https://brainly.com/question/23847661
#SPJ2
