Calculus Derivatives

Power Rule

The derivative of x raised to the power of n is n times x raised to the power of (n-1).

Derivative of x^n

The derivative of x raised to the power of n is n times x raised to the power of (n-1).

Cosine Function

The derivative of the cosine function is -sin(x).

Derivative of Sine Function

The derivative of the sine function is cosine(x).

Negative Sine Function

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

Derivative of Cosine Function

The derivative of the cosine function is -sin(x).

Secant Squared Function

The derivative of secant squared is sec(x) * tan(x).

Derivative of Tangent Function

The derivative of the tangent function is sec^2(x).

Negative Cosecant Cotangent Function

The derivative of -csc(x)cot(x) is csc(x)^2.

Derivative of Cosecant Function

The derivative of the cosecant function is -csc(x)cot(x).

Secant Tangent Function

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

Derivative of Secant Function

The derivative of the secant function is sec(x)tan(x).

Exponential Function

The derivative of a^x is a^x * ln(a).

Derivative of Exponential Function

The derivative of e^x is e^x.

Natural Logarithm Function

The derivative of ln(x) is 1/x.

Derivative of Logarithmic Function

The derivative of log_a(x) is 1/(xln(a)).

Inverse Trigonometric Function

The derivative of arcsin(u) is u'/(sqrt(1-u^2)).

Inverse Trigonometric Function

The derivative of arccos(u) is -u'/(sqrt(1-u^2)).

Inverse Trigonometric Function

The derivative of arctan(u) is u'/(1+u^2).

Inverse Trigonometric Function

The derivative of arccot(u) is -u'/(1+u^2).

Inverse Trigonometric Function

The derivative of arcsec(u) is u'/(abs(u)sqrt(u^2-1)).

Inverse Trigonometric Function

The derivative of arccsc(u) is -u'/(abs(u)sqrt(u^2-1)).