General Differentiation
Function

Derivative

sinx

cosx

cosx

sinx

sin^{2}x

2∙sinx∙cosx = sin^{2}x

cos^{2}x

2∙sinx∙cosx =  sin^{2}x

tanx = sec^{2}x

1/(cos^{2}x) = 1+tan^{2}x

cotx = csc^{2}x

1/(sin^{2}x) = 1cot^{2}x

secx

secx∙tanx

cscx

cscx∙cotx

arcsinx = sin^{1}x

1/√(1x^{2})

arccosx = cos^{1}x

1/√(1x^{2})

arctanx = tan^{1}x

1/(1+x^{2})

arccotx = cot^{1}x

1/(1+x^{2})

arcsecx = sec^{1}x

1/(x∙√(x^{2}1))

arccscx = csc^{1}x

1/(x∙√(x^{2}1))

The following table summarizes the derivatives of the six trigonometric functions, as well as their chain rule counterparts (that is, the sine, cosine, etc. of a function).
Example 1:
Example 2: Find the derivative of y = 3 sin^{3} (2x^{4} + 1).
Put u = 2x^{4} + 1 and v = sin u
So y = 3v^{3}
Example 3: Differentiate
Apply the quotient rule first, then we have
Now apply the product rule in the first part of the numerator, the result of g'(x) will be:
Example 4: Differentiate y = cos^{3}(tan(3x)).
Apply the chain rule four times: