Differentiating sin, cos and tan

Differentiating sin, cos and tan

Differentiating sine, cosine and tangent

Sine Differentiation Rules

• The derivative of sine (sin) function is cosine (cos).
• Rule: If y = sin x, then dy/dx = cos x.
• This rule applies to any variable multiplication inside the sin function, with the chain rule. For instance, for y = sin 2x, dy/dx = 2cos 2x.

Cosine Differentiation Rules

• The derivative of cosine (cos) function is negative sine (-sin).
• Rule: If y = cos x, then dy/dx = -sin x.
• This rule applies to variable multiplication inside the cos function, again with the chain rule. For example, for y = cos 3x, dy/dx = -3sin 3x.

Tangent Differentiation Rules

• The derivative of tangent (tan) function is sec²x.
• Rule: If y = tan x, then dy/dx = sec²x.
• Tangent differentiation also adheres to the chain rule when dealing with variable multiplication inside the function. For instance, for y = tan 4x, dy/dx = 4sec² 4x.