Chapter 3 : Derivatives. For problems 1 – 12 find the derivative of the given function. Retrouvez infos & avis sur une large sélection de DVD & Blu-ray neufs ou d'occasion. (Optional), Maplesoft™, filiale de Cybernet Systems Co. Ltd. au Japon, est le premier fournisseur logiciels haute performance dans le domaine de l'ingénierie, des sciences et des mathématiques. the derivative of 1f = −f’f 2. Why Math. The Student[Calculus1] package contains two routines that can be used to both work with and visualize the concepts of Newton quotients and derivatives. A la recherche de Maple T.A. If you're seeing this message, it means we're having trouble loading external resources on our website. Sketch one period of the velocity function for $t \geq 0$ .d. While any command in the package can be referred to using the long form, for example, Student[Calculus1][DerivativePlot],  it is easier, and often clearer, to load the package, and then use the short form command names. Product and Quotient Rule – In this section we will give two of the more important formulas for differentiating functions. We discuss the rate of change of a function, the velocity of a moving object and the slope of the tangent line to a graph of a function. Our mission is to provide a free, world-class education to anyone, anywhere. • Conditions d'utilisation | Confidentialité | Marques déposées | Site Map. © 2020 Why Math. While any command in the package can be referred to using the long form, for example. y = 2t4 −10t2+13t y = 2 t 4 − 10 t 2 + 13 t Solution. Calculus 1. En savoir plus sur Maplesoft, Langue: Save my name, email, and website in this browser for the next time I comment. Section 3-3 : Differentiation Formulas. I will be moderating the course as you progress and will be happy to provide videos or explanations for any additional questions. Your feedback will be used Feel free to use the lessons you need and skip those that you don’t. Derivative rules: constant, sum, difference, and constant multiple, Combining the power rule with other derivative rules, Derivatives of cos(x), sin(x), ˣ, and ln(x). For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=x^{2}-\sec x+1$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=3 \csc x+\frac{5}{x}$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=x^{2} \cot x$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=x-x^{3} \sin x$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=\frac{\sec x}{x}$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=\sin x \tan x$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=(x+\cos x)(1-\sin x)$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=\frac{\tan x}{1-\sec x}$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=\frac{1-\cot x}{1+\cot x}$$, For the following exercises, find $\frac{d y}{d x}$ for the given functions.$$y=\cos x(1+\csc x)$$, For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of $x .$ Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct.$$[\mathbf{T}] f(x)=-\sin x, x=0$$, For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of $x .$ Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct.$$[\mathbf{T}] f(x)=\csc x, x=\frac{\pi}{2}$$, For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of $x .$ Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct.$$[\mathbf{T}] f(x)=1+\cos x, x=\frac{3 \pi}{2}$$, For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of $x .$ Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct.$$[\mathbf{T}] f(x)=\sec x, x=\frac{\pi}{4}$$, For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of $x .$ Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct.$$[\mathbf{T}] f(x)=x^{2}-\tan x x=0$$, For the following exercises, find the equation of the tangent line to each of the given functions at the indicated values of $x .$ Then use a calculator to graph both the function and the tangent line to ensure the equation for the tangent line is correct.$$[\mathbf{T}] f(x)=5 \cot x x=\frac{\pi}{4}$$, For the following exercises, find $\frac{d^{2} y}{d x^{2}}$ for the given functions.$$y=x \sin x-\cos x$$, For the following exercises, find $\frac{d^{2} y}{d x^{2}}$ for the given functions.$$y=\sin x \cos x$$, For the following exercises, find $\frac{d^{2} y}{d x^{2}}$ for the given functions.$$y=x-\frac{1}{2} \sin x$$, For the following exercises, find $\frac{d^{2} y}{d x^{2}}$ for the given functions.$$y=\frac{1}{x}+\tan x$$, For the following exercises, find $\frac{d^{2} y}{d x^{2}}$ for the given functions.$$y=2 \csc x$$, For the following exercises, find $\frac{d^{2} y}{d x^{2}}$ for the given functions.$$y=\sec ^{2} x$$.

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