Domanda del libro di testo
72–76. Tangent lines Find an equation of the line tangent to each of the following curves at the given point.
y = 3x³+ sin x; (0, 0)
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Ch. 3 - Derivatives
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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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.R.17
9–61. Evaluate and simplify y'.
y = 5t² sin t
Guida verificata passo dopo passo1
First, identify the given function y = 5t² sin(t). We need to find the derivative y' with respect to t.
Apply the product rule for differentiation, which states that if you have a function u(t) * v(t), its derivative is u'(t) * v(t) + u(t) * v'(t). Here, u(t) = 5t² and v(t) = sin(t).
Differentiate u(t) = 5t² with respect to t. The derivative is u'(t) = 10t.
Differentiate v(t) = sin(t) with respect to t. The derivative is v'(t) = cos(t).
Combine the results using the product rule: y' = u'(t) * v(t) + u(t) * v'(t) = 10t * sin(t) + 5t² * cos(t). Simplify the expression if possible.
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Differentiation
Differentiation is a fundamental concept in calculus that involves finding the derivative of a function. The derivative represents the rate of change of the function with respect to its variable. In this case, we need to differentiate the function y = 5t² sin t to find y'.
Video consigliato:
Percorso guidato
05:53
Finding Differentials
Product Rule
The Product Rule is a specific rule used in differentiation when dealing with the product of two functions. It states that if you have two functions u(t) and v(t), the derivative of their product is given by u'v + uv'. In the given function y = 5t² sin t, we will apply the Product Rule to differentiate the product of 5t² and sin t.
Video consigliato:
05:18The Product Rule
Trigonometric Functions
Trigonometric functions, such as sine and cosine, are fundamental functions in calculus that describe relationships in triangles and periodic phenomena. The derivative of sin t is cos t, which is essential for differentiating the sin t component in the function y = 5t² sin t. Understanding how to differentiate these functions is crucial for solving the problem.
Video consigliato:
Percorso guidato
6:04Introduction to Trigonometric Functions
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