Integrals and Derivatives of trigonometry

What is the derivative of sin(x)?

The derivative of sin(x) is cos(x)

What is the derivative of cos(x)?

The derivative of cos(x) is -sin(x)

What is the derivative of tan(x)?

The derivative of tan(x) is sec²(x)

What is the integral of sin(x)?

The integral of sin(x) is -cos(x) + C

What is the integral of cos(x)?

The integral of cos(x) is sin(x) + C

What is the integral of sec²(x)?

The integral of sec²(x) is tan(x) + C

What is the derivative of csc(x)?

The derivative of csc(x) is -csc(x)cot(x)

What is the derivative of sec(x)?

The derivative of sec(x) is sec(x)tan(x)

What is the integral of csc(x)?

The integral of csc(x) is -ln|csc(x) + cot(x)| + C

What is the integral of sec(x)?

The integral of sec(x) is ln|sec(x) + tan(x)| + C

What is the integral of cos(a*x)?

The integral of cos(ax) is (1/a)sin(ax) + C

What is the derivative of sin(a*x)?

The derivative of sin(ax) is acos(a*x)

What is the integral of sin(a*x)?

The integral of sin(ax) is -(1/a)cos(ax) + C

What is the derivative of tan(a*x)?

The derivative of tan(ax) is asec²(a*x).

What is the integral of cot(x)?

The integral of cot(x) is ln|sin(x)| + C.

What is the integral of sec(x)tan(x)?

The integral of sec(x)tan(x) is sec(x) + C.

What is the derivative of csc(x)?

The derivative of csc(x) is -csc(x)cot(x).

What is the integral of csc²(x)?

The integral of csc²(x) is -cot(x) + C.

What is the derivative of sec²(x)?

The derivative of sec²(x) is 2sec²(x)tan(x).

What is the integral of sec(x)sec(x)?

The integral of sec²(x) is tan(x) + C.

What is the derivative of arcsin(x)?

The derivative of arcsin(x) is 1/√(1-x²).

What is the integral of tan(x)?

The integral of tan(x) is -ln|cos(x)| + C.

What is the derivative of arccos(x)?

The derivative of arccos(x) is -1/√(1-x²).

What is the integral of arctan(x)?

The integral of arctan(x) is x*arctan(x) - (1/2)ln(1+x²) + C.

What is the derivative of arccot(x)?

The derivative of arccot(x) is -1/(1+x²).

What is the integral of sec(x)?

The integral of sec(x) is ln|sec(x) + tan(x)| + C.

What is the derivative of sin²(x)?

The derivative of sin²(x) is 2sin(x)cos(x) = sin(2x).

What is the integral of cos²(x)?

The integral of cos²(x) is (1/2)(x + sin(x)cos(x)) + C.

What is the derivative of cos(a*x)?

The derivative of cos(ax) is -asin(a*x).

What is the integral of sin²(x)?

The integral of sin²(x) is (1/2)(x - sin(x)cos(x)) + C.

What is the derivative of a*sec(x)?

The derivative of asec(x) is asec(x)*tan(x).

What is the integral of csc(x)?

The integral of csc(x) is -ln|csc(x) + cot(x)| + C.

What is the derivative of tan²(x)?

The derivative of tan²(x) is 2tan(x)sec²(x).

What is the integral of sinh(x)?

The integral of sinh(x) is cosh(x) + C.

What is the derivative of sinh(x)?

The derivative of sinh(x) is cosh(x).

What is the integral of cosh(x)?

The integral of cosh(x) is sinh(x) + C.

What is the derivative of cosh(x)?

The derivative of cosh(x) is sinh(x).

What is the integral of e^x*sin(x)?

The integral of e^xsin(x) is (e^x(sin(x) - cos(x)))/2 + C.

What is the derivative of ln(sin(x))?

The derivative of ln(sin(x)) is cot(x).

What is the integral of ln(x)?

The integral of ln(x) is xln(x) - x + C.