Tutorial Exercise dy Calculate Simplify your answer. HINT [See Examples 1 and 2.] dx y = 2x(3x² - 1) Step 1 In the given equation y = 2x(3x² - 1) we have the product of two differentiable functions of x: 2x and (3x² - 1). Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies. [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function. g'(x) g(x) + f(x). [(x)9(x)] = f'(x) derivative of first second first derivative of second d dx For the given equation y = 2x(3x² - 1), if we let f(x) = 2x and g(x) = 3x² - 1, then y = 2x(3x2 - 1) = f(x) · g(x). In other words, we can define f(x) = 2x as the first function and g(x) = 3x²1 as the second function. dy Note that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x or dx As a precursor to using the product rule, complete the following statements. If f(x) = 2x, then f'(x) = If g(x)=3x21, then g'(x) =
Tutorial Exercise dy Calculate Simplify your answer. HINT [See Examples 1 and 2.] dx y = 2x(3x² - 1) Step 1 In the given equation y = 2x(3x² - 1) we have the product of two differentiable functions of x: 2x and (3x² - 1). Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies. [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function. g'(x) g(x) + f(x). [(x)9(x)] = f'(x) derivative of first second first derivative of second d dx For the given equation y = 2x(3x² - 1), if we let f(x) = 2x and g(x) = 3x² - 1, then y = 2x(3x2 - 1) = f(x) · g(x). In other words, we can define f(x) = 2x as the first function and g(x) = 3x²1 as the second function. dy Note that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x or dx As a precursor to using the product rule, complete the following statements. If f(x) = 2x, then f'(x) = If g(x)=3x21, then g'(x) =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Tutorial Exercise
Calculate
=
dy
dx
Step 1
In the given equation y = 2x(3x² - 1) we have the product of two differentiable functions of x: 2x and (3x² − 1).
Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies.
dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
=
Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function.
g'(x)
f'(x) · g(x) + f(x).
derivative of first second first derivative of second
Simplify your answer. HINT [See Examples 1 and 2.]
y =
If f(x)
=
2x(3ײ – 1)
For the given equation y = 2x(3x² − 1), if we let f(x) = 2x and g(x) = 3x² – 1, then y = 2x(3x² − 1) = f(x) · g(x). In other words, we can define f(x) = 2x as the first function and
g(x)
3x²
1 as the second function.
d [f(x)g(x)
dx
-
dy
Note that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x or
dx
=
As a precursor to using the product rule, complete the following statements.
2x, then f'(x) =
=
If g(x) = 3x² - 1, then g'(x) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd48171ba-d1cc-47b1-bf9c-8041143384f0%2Fc7cbfba4-43c3-418b-9eef-209965f16e59%2Ffqa62mi_processed.png&w=3840&q=75)
Transcribed Image Text:Tutorial Exercise
Calculate
=
dy
dx
Step 1
In the given equation y = 2x(3x² - 1) we have the product of two differentiable functions of x: 2x and (3x² − 1).
Therefore, to differentiate we must first recall the Product Rule which states that if f and g are differentiable functions of x, then so is their product fg, and the following formula applies.
dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
=
Many like to remember that the derivative of a product is the derivative of the first function times the second function plus the first function times the derivative of the second function.
g'(x)
f'(x) · g(x) + f(x).
derivative of first second first derivative of second
Simplify your answer. HINT [See Examples 1 and 2.]
y =
If f(x)
=
2x(3ײ – 1)
For the given equation y = 2x(3x² − 1), if we let f(x) = 2x and g(x) = 3x² – 1, then y = 2x(3x² − 1) = f(x) · g(x). In other words, we can define f(x) = 2x as the first function and
g(x)
3x²
1 as the second function.
d [f(x)g(x)
dx
-
dy
Note that since y is the product of two differentiable functions, we can use the product rule to find the derivative of y with respect to x or
dx
=
As a precursor to using the product rule, complete the following statements.
2x, then f'(x) =
=
If g(x) = 3x² - 1, then g'(x) =
Expert Solution
Step 1
The derivative of the function is to be calculated.
According to the product rule, for two differentiable functions f(x) and g(x), the derivative of their product is given by:
Step by step
Solved in 2 steps
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