Calculus Derivatives and Trigonometric Functions: Key Rules and Formulas

What is the derivative of the product of two functions f(x) and g(x)?

d/dx [f(x) · g(x)] = f'(x)g(x) + f(x)g'(x)

What is the derivative of the quotient of two functions f(x) and g(x)?

d/dx [f(x)/g(x)] = (f'(x)g(x) - f(x)g'(x)) / (g(x))²

What is the derivative of the composition of two functions f(g(x))?

d/dx [f(g(x))] = f'(g(x)) g'(x)

What is the derivative of the natural logarithm of x?

d/dx [ln(x)] = 1/x

What is the derivative of the sine function sin(x)?

d/dx [sin(x)] = cos(x)

What is the derivative of the cosine function cos(x)?

d/dx [cos(x)] = -sin(x)

What is the derivative of the tangent function tan(x)?

d/dx [tan(x)] = sec²(x)

What is the derivative of the cotangent function cot(x)?

d/dx [cot(x)] = -csc²(x)

What is the derivative of the secant function sec(x)?

d/dx [sec(x)] = sec(x)tan(x)

What is the derivative of the cosecant function csc(x)?

d/dx [csc(x)] = -csc(x)cot(x)

What is the derivative of the arcsine function arcsin(x)?

d/dx [arcsin(x)] = 1/√(1-x²)

What is the derivative of the arccosine function arccos(x)?

d/dx [arccos(x)] = -1/√(1-x²)

What is the derivative of the arctangent function arctan(x)?

d/dx [arctan(x)] = 1/(1+x²)

What is the derivative of the arccotangent function arccot(x)?

d/dx [arccot(x)] = -1/(1+x²)

What is the derivative of the arcsecant function arcsec(x)?

d/dx [arcsec(x)] = 1/(|x|√(x²-1))

What is the derivative of the arccosecant function arccsc(x)?

d/dx [arccsc(x)] = -1/(|x|√(x²-1))

What is the derivative of a^x

d/dx [a^x] = (a^x)(ln(a))

What is the derivative of loga(x)

d/dx [loga(x)] = 1/aln(x)