Is there any review of all the derivative in only one test

PearsonReview comes out with a book every year on the subjects of the AP Test. Within the book there are a few comprehensive practice testz which I found helpful. when I was studying. You can find a copy at you local library or buy one on amazon.

whats the "arc" in arctan arccos arcsine is it by accident ?

The "arc" part just means that it is the inverse of that trig identity. Arctan=tan^(-1)(x) which is the inverse of tan, arccos= cos^(-1)(x) which is the inverse of cosine, and arcsin=sin^(-1)(x) which is the inverse of sine.

Main content

Class 12 math (India)

Course: Class 12 math (India) > Unit 5

Lesson 16: Derivatives capstone

Common derivatives review

Google Classroom

Review the differentiation rules for all the common function types.

Polynomials

\frac{d}{d x} (a x^{n}) = a \cdot n x^{n - 1}

Want to learn more about differentiating polynomials? Check out this video.

Radicals

\frac{d}{d x} \sqrt[m]{x^{n}} = \frac{d}{d x} (x^{^{\frac{n}{m}}}) = \frac{n}{m} x^{^{\frac{n}{m} - 1}}

Want to learn more about differentiating radicals? Check out this video.

Trigonometric functions

\frac{d}{d x} \sin (x) = \cos (x)

\frac{d}{d x} \cos (x) = - \sin (x)

\frac{d}{d x} \tan (x) = \sec^{2} (x) = \frac{1}{\cos^{2} (x)}

\frac{d}{d x} \cot (x) = - \csc^{2} (x) = - \frac{1}{\sin^{2} (x)}

\frac{d}{d x} \sec (x) = \sec (x) \tan (x) = \frac{\sin (x)}{\cos^{2} (x)}

\frac{d}{d x} \csc (x) = - \csc (x) \cot (x) = - \frac{\cos (x)}{\sin^{2} (x)}

Want to learn more about differentiating trigonometric functions? Check out this video about sine and cosine, this video about tangent and cotangent, and this video about secant and cosecant.

Exponential functions

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (a^{x}) = \ln (a) \cdot a^{x}

Want to learn more about differentiating exponential functions? Check out this video.

Logarithmic functions

\frac{d}{d x} \ln (x) = \frac{1}{x}

\frac{d}{d x} \log_{b} (x) = \frac{1}{\ln (b) x}

Want to learn more about differentiating logarithmic functions? Check out this video.

Inverse trigonometric functions

\frac{d}{d x} \arcsin (x) = \frac{1}{\sqrt{1 - x^{2}}}

\frac{d}{d x} \arccos (x) = - \frac{1}{\sqrt{1 - x^{2}}}

\frac{d}{d x} \arctan (x) = \frac{1}{1 + x^{2}}

Want to learn more about differentiating inverse trigonometric functions? Check out this video about the inverse sine, this video about the inverse cosine, and this video about the inverse tangent.

Want to join the conversation?

Sort by:

Dorcas Okese
Posted 7 years ago. Direct link to Dorcas Okese's post “Is there any review of al...”
Is there any review of all the derivative in only one test
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Austin Omlor
  Posted 7 years ago. Direct link to Austin Omlor's post “PearsonReview comes out w...”
  PearsonReview comes out with a book every year on the subjects of the AP Test. Within the book there are a few comprehensive practice testz which I found helpful. when I was studying. You can find a copy at you local library or buy one on amazon.
  Comment on Austin Omlor's post “PearsonReview comes out w...”
  (8 votes)
soraith
Posted 6 years ago. Direct link to soraith's post “whats the "arc" in arctan...”
whats the "arc" in arctan arccos arcsine is it by accident ?
Button navigates to signup pageButton navigates to signup page
(0 votes)
Answer
- tammyla101
  Posted 6 years ago. Direct link to tammyla101's post “The "arc" part just means...”
  The "arc" part just means that it is the inverse of that trig identity. Arctan=tan^(-1)(x) which is the inverse of tan, arccos= cos^(-1)(x) which is the inverse of cosine, and arcsin=sin^(-1)(x) which is the inverse of sine.
  Button navigates to signup page
  (5 votes)