Domanda del libro di testo
27–40. Implicit differentiation Use implicit differentiation to find dy/dx.
y = xe^y
305
views
Ch. 3 - Derivatives
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 3.5.23
Find the derivative of the following functions.
y = sin x + cos x
Guida verificata passo dopo passo1
Identify the function for which you need to find the derivative: \( y = \sin x + \cos x \).
Recall the basic derivatives of trigonometric functions: \( \frac{d}{dx}(\sin x) = \cos x \) and \( \frac{d}{dx}(\cos x) = -\sin x \).
Apply the sum rule for derivatives, which states that the derivative of a sum of functions is the sum of their derivatives.
Differentiate each term separately: \( \frac{d}{dx}(\sin x) = \cos x \) and \( \frac{d}{dx}(\cos x) = -\sin x \).
Combine the results to find the derivative of the entire function: \( \frac{dy}{dx} = \cos x - \sin x \).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Derivative
The derivative of a function measures how the function's output value changes as its input value changes. It is a fundamental concept in calculus that represents the slope of the tangent line to the curve of the function at any given point. Derivatives are used to find rates of change and can be computed using various rules and techniques.
Video consigliato:
Percorso guidato
05:44
Derivatives
Trigonometric Functions
Trigonometric functions, such as sine (sin) and cosine (cos), are fundamental functions in mathematics that relate angles to ratios of sides in right triangles. In calculus, these functions have specific derivatives: the derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x). Understanding these derivatives is essential for differentiating functions involving trigonometric expressions.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
Sum Rule of Derivatives
The sum rule of derivatives states that the derivative of a sum of functions is equal to the sum of their derivatives. This means that if you have a function that is the sum of two or more functions, you can differentiate each function separately and then add the results together. This rule simplifies the process of finding derivatives for functions like y = sin x + cos x.
Video consigliato:
Percorso guidato
05:44Algebra Rules for Finite Sums
Pratica correlata
Domanda del libro di testo
23–51. Calculating derivatives Find the derivative of the following functions.
y = sin x / 1 + cos x
313
views
Domanda del libro di testo
If f is continuous at a, must f be differentiable at a?
453
views
Domanda del libro di testo
A water heater that has the shape of a right cylindrical tank with a radius of 1 ft and a height of 4 ft is being drained. How fast is water draining out of the tank (in ft³/min) if the water level is dropping at 6 min/in?
222
views
Domanda del libro di testo
Use the graph of f(x)=|x| to find f′(x).
602
views
Domanda del libro di testo
Find the slope of the graph of f(x) = 2 + xe^x at the point (0, 2).
294
views