[07.2 Derivatives 02]
Derivative of a Variable to the First Power
$$\frac{d}{{dx}}x = 1$$
[13.1 Probability 4]
[02.7 Trigonometry 1]
[01.3 Relations and Functions 3]
[07.1 Integrals 9]
Integrals of Derivatives
$$\large \int\limits_a^b {\frac{d}{{dx}}F\left( x \right)dx} = F\left( b \right) - F\left( a \right)$$
[09.1 Differentials 3]
[07.2 Derivatives 06]
Derivative of a natural logarithm
$$\frac{d}{{dx}}\ln \left( x \right) = \frac{1}{x}$$
[07.2 Derivatives 05]
Derivative of a base exponential
$$\frac{d}{{dx}}b^x = b^x \ln \left( b \right)$$
[02.7 Trigonometry 6]
[07.2 Derivatives 07]
Derivative of a sine
$$\frac{d}{{dx}}\sin x = \cos x$$
[07.1 Integrals 1]
Integration by Parts
$$\large \int {u\frac{{dv}}{{dx}}} dx = uv - \int {\frac{{du}}{{dx}}} vdx$$
[13.1 Probability 1]
[02.7 Trigonometry 4]
[01.4 Relations and Functions 4]
[01.2 Relations and Functions 2]
[13.1 Probability 2]
[02.7 Trigonometry 5]
Integral of Sine
$$\large \int {\sin (ax)} dx = - \frac{1}{a}\cos (ax) + c$$
[99.2 Exam Strategies 2]
[13.1 Probability 3]
[07.5 Graph 4]
[07.1 Integrals 5]
Integral of Sine
$$\large \int {\sin (ax)} dx = - \frac{1}{a}\cos (ax) + c$$
[07.5 Graph 2]
[07.5 Graph 5]
[07.1 Integrals 8]
Integral of Secant
$$\large\int {\sec (ax)} dx = \frac{1}{a}\ln \left| {\tan \left( {\frac{{ax}}{2} + \frac{\pi }{4}} \right)} \right| + c$$
[01.1 Relations and Functions 1]
[07.2 Derivatives 03]
Derivative of a Variable to the nth Power
$$\frac{d}{{dx}}x^n = nx^{\left( {n - 1} \right)}$$
[07.2 Derivatives 09]
Derivative of a Tangent
$$\frac{d}{{dx}}\tan x = \sec ^2 x$$
[07.2 Derivatives 04]
Derivative of an exponential
$$\frac{d}{{dx}}e^{ax} = ae^{ax}$$
[07.1 Integrals 3]
Integral of Reciprocal
$$\large \int {\frac{1}{x}} dx = \ln \left| x \right| + c$$
[02.7 Trigonometry 3]
[07.2 Derivatives 08]
Derivative of a cosine
$$\frac{d}{{dx}}\cos x = - \sin x$$
[07.1 Integrals 2]
Integral of powers not equal to -1
$$\large \int {x^n } dx = \frac{{x^{n + 1} }}{{n + 1}},(n \ne - 1)$$
[07.5 Graph 3]
[07.2 Derivatives 10]
Derivative of a CoTangent
$$\frac{d}{{dx}}\cot x = - \csc ^2 x$$
[09.1 Differentials 2]
[07.1 Integrals 7]
Integral of Cosecant
$$\large
\int {\csc (ax)} dx = \frac{1}{a}\ln \left| {\tan \left( {\frac{{ax}}{2}} \right)} \right| + c
$$
[07.1 Integrals 4]
Integral of Cosine
$$\large \int {\frac{1}{x}} dx = \ln \left| x \right| + c$$
[07.1 Integrals 6]
Integral of Tangent
$$\large\int {\tan (ax)} dx = - \frac{1}{a}\ln \left| {\cos (ax)} \right| + c$$
[07.2 Derivatives 01]
Derivative of a constant
$$\frac{d}{dx}C = 0$$
[13.1 Probability 5]
[07.5 Graph 1]
[02.7 Trigonometry 2]
[09.1 Differentials 1]
[99.2 Exam Strategies 1]
