View Derivative Formula Sheet 2020.pdf from MAT 10273 at Gwinnett Technical College. Substitute x and y with given point’s coordinates i.e here ‘0’ as x and ‘b’ as y, Your email address will not be published. August 17 @ d d x ( s i n − 1 x) = 1 √ 1 − x 2, − 1 < x < 1. d dx(cos − 1x) = − 1 √1 − x2, − 1 < x < 1. d d x ( c o s − 1 x) = − 1 √ 1 − x 2, − 1 < x < 1. d dx(tan − 1x) = 1 1 + x2. Calculus I Formulas MAC 2311 1. He is the author of Calculus Workbook For Dummies, Calculus Essentials For Dummies, and three books on geometry in the For Dummies series. ∫e du =eu +C Example 2: Evaluate ∫( ) 4x2 −5x3 +12 dx To evaluate this problem, use the first four Integral Formulas. d d x ( t a n − 1 x) = 1 1 + x 2. d dx(cot − 1x) = − 1 1 + x2. 2) $$\frac{d}{{dx}}{x^n} = n{x^{n – 1}}$$ is called the Power Rule of Derivatives. Differentiation rules 3. Provided by the Academic Center for Excellence 3 Common Derivatives and Integrals 4. , 1 1 1 + ≠− + ∫ = + C n n u u du n n 5. 5) d d x x = 1 2 x. If yfx then all of the following are equivalent notations for the derivative. ;Derivative of a Constant: :=0 2Sum/Difference Rule: : ± ; ′= ′± ;Constant Out: ′ :⋅ ′=⋅ Product Rule: : ⋅ ;′= ′ ⋅ + ′ Quotient Rule: @ A ′ = ′⋅ − ′⋅ Chain Rule: : ; = ⋅ Common Derivatives: : ln : ; ;=1 : ln :|| ; ;=1 : ;= Applications of Differentiation 4. General Derivative Formulas: 1) d d x ( c) = 0 where c is any constant. 11) $$\frac{d}{{dx}}\ln x = \frac{1}{x}$$, 12) $$\frac{d}{{dx}}{\log _a}x = \frac{1}{{x\ln a}}$$, 13) $$\frac{d}{{dx}}\ln f(x) = \frac{1}{{f(x)}}\frac{d}{{dx}}f(x)$$, 14) $$\frac{d}{{dx}}{\log _a}f(x) = \frac{1}{{f(x)\ln a}}\frac{d}{{dx}}f(x)$$, 16) $$\frac{d}{{dx}}{e^{f(x)}} = {e^{f(x)}}\frac{d}{{dx}}f(x)$$, 18) $$\frac{d}{{dx}}{a^{f(x)}} = {a^{f(x)}}\ln a\frac{d}{{dx}}f(x)$$, 19) $$\frac{d}{{dx}}{x^x} = {x^x}(1 + \ln x)$$, 23) $$\frac{d}{{dx}}Cotx = – Co{\sec ^2}x$$, 24) $$\frac{d}{{dx}}Secx = Secx \cdot Tanx$$, 25) $$\frac{d}{{dx}}Co\sec x = – Co\sec x \cdot Cotx$$, 29) $$\frac{d}{{dx}}Cothx =- Co\sec {h^2}x$$, 30) $$\frac{d}{{dx}}Sechx =- Sechx \cdot Tanhx$$, 31) $$\frac{d}{{dx}}Ce\sec hx =- Co\sec hx \cdot Cothx$$. Limits and Derivatives 2. 4) d d x [ f ( x)] n = n [ f ( x)] n – 1 d d x f ( x) is the Power Rule for Functions. Derivative of Inverse Trigonometric Functions: 32) $$\frac{d}{{dx}}Si{n^{ – 1}}x = \frac{1}{{\sqrt {1 – {x^2}} }},{\text{ }} – 1 < x < 1$$, 33) $$\frac{d}{{dx}}Co{s^{ – 1}}x = \frac{{ – 1}}{{\sqrt {1 – {x^2}} }},{\text{ }} – 1 < x < 1$$, 34) $$\frac{d}{{dx}}Ta{n^{ – 1}}x = \frac{1}{{1 + {x^2}}}$$, 35) $$\frac{d}{{dx}}Co{t^{ – 1}}x = \frac{{ – 1}}{{1 + {x^2}}}$$, 36) $$\frac{d}{{dx}}Se{c^{ – 1}}x = \frac{1}{{x\sqrt {{x^2} – 1} }},{\text{ }}\left| x \right| > 1$$, 37) $$\frac{d}{{dx}}Co{\sec ^{ – 1}}x = \frac{{ – 1}}{{x\sqrt {{x^2} – 1} }},{\text{ }}\left| x \right| > 1$$. ** POWER-REDUCING FORMULAS cos² x = x 1 cos2x sin² x = x 1 cos2x SPECIAL LIMITS 0 x sin x lim x 0 x def n n x n lim (1 ) e L’HOSPITAL’S RULE If you are asked to take the limit of a rational function (x) ƒ(x) lim x a g, where ƒ(x) and g(x) are differentiable, but the limit comes to 0 … It really helps us a lot. Ryan has taught junior high and high school math since 1989. in simple, the derivative of the derivative. Derivatives Formula Sheet.pdf - Calculus:DerivativeFormulas NonChainRule ChainRule d n X n X n1 dx d sin x cos x dx d cos x sin x d dx d tan x sec 2 x Some of the general differentiation formulas are; Power Rule: (d/dx) (x n ) = nx n-1; Derivative of a constant, a: (d/dx) (a) = 0; Derivative of a constant multiplied with function f: (d/dx) (a. f) = af’ Sum Rule: (d/dx) (f ± g) = f’ ± g’ Product Rule: (d/dx) (fg)= fg’ + gf’ 11:20 am, Firstly u have take the derivative of given equation w.r.t x. 4) $$\frac{d}{{dx}}{[f(x)]^n} = n{[f(x)]^{n – 1}}\frac{d}{{dx}}f(x)$$ is the Power Rule for Functions. Please tell me how can I make this better. He lives in Evanston, Illinois. Welcome to MathPortal. Derivatives Cheat Sheet Derivative Rules 1. Constant Rule: d dx (c) = 0; where c is a constant 2. Power Rule: d dx (xn) = nxn 1 3. dy/dx of y= x^3+29 is 3x^2 then d^2y/dx^2 will be 6x. This web site owner is mathematician Miloš Petrović. 4:57 pm. Product Rule: (fg)0 = f0g +fg0 4. July 26 @ Vhia Berania Limits and Derivatives Class 11 Formulas & Notes are cumulated by our panel of highly experienced teachers to provide the students with effective exam preparation. Quotient Rule: f g 0 = f0g 0fg g2 5. Integrals 5. Derivative of Inverse Hyperbolic Functions: 38) $$\frac{d}{{dx}}Sin{h^{ – 1}}x = \frac{1}{{\sqrt {1 + {x^2}} }}$$, 39) $$\frac{d}{{dx}}Cos{h^{ – 1}}x = \frac{1}{{\sqrt {{x^2} – 1} }}$$, 40) $$\frac{d}{{dx}}Tan{h^{ – 1}}x = \frac{1}{{1 – {x^2}}},{\text{ }}\left| x \right| < 1$$, 41) $$\frac{d}{{dx}}Cot{h^{ – 1}}x = \frac{1}{{{x^2} – 1}},{\text{ }}\left| x \right| > 1$$, 42) $$\frac{d}{{dx}}Sec{h^{ – 1}}x = \frac{{ – 1}}{{x\sqrt {1 – {x^2}} }},{\text{ }}0 < x < 1$$, 43) $$\frac{d}{{dx}}Co\sec {h^{ – 1}}x = \frac{{ – 1}}{{x\sqrt {1 + {x^2}} }},{\text{ }}x > 0$$, Khushi Shrestha