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Differentiate. Step 1 F(y) x) = (1/²2 - 11/2) (v + 8y²³) To find the derivative of the product F(y) = Step 2 d [f(y)g(y)] = f'(y)g(y) + f(y)g'(y). dy First, we rewrite the first term of the product as follows. 1 4 V4 y² - = y -2✔ The derivative of the first term, F'(y) = 1 +16 Step 4 Now, using the Product Rule, 4y 4 (1/2 - 1/4)(x₁ (y + 8y³), we will use the Product Rule, which states 1+24y2 Step 3 Next, the derivative of the second term, y + 8y³, is 1+24y² =y-2_4y-4, is 16 -4 -5 + 16y-5)(y + 8y³) + (y-2 - 4y−4)(1 + 24,²).

Differentiate. Step 1 F(y) x) = (1/²2 - 11/2) (v + 8y²³) To find the derivative of the product F(y) = Step 2 d [f(y)g(y)] = f'(y)g(y) + f(y)g'(y). dy First, we rewrite the first term of the product as follows. 1 4 V4 y² - = y -2✔ The derivative of the first term, F'(y) = 1 +16 Step 4 Now, using the Product Rule, 4y 4 (1/2 - 1/4)(x₁ (y + 8y³), we will use the Product Rule, which states 1+24y2 Step 3 Next, the derivative of the second term, y + 8y³, is 1+24y² =y-2_4y-4, is 16 -4 -5 + 16y-5)(y + 8y³) + (y-2 - 4y−4)(1 + 24,²).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Differentiate. Step 1 F(y) ²(x) = (1/27 - 12/2) (X + 8 To find the derivative of the product F(y) = (1/12 - 11/17) (1 Step 2 d [f(y)g(y)] = f'(y)g(y) + f(y)g'(y). dy First, we rewrite the first term of the product as follows. 1 4 V4 The derivative of the first term, -3 F'(y) = Step 4 Now, using the Product Rule, +16 F'(y) = -2 1 4y 4 4 y 1+24y² Step 3 Next, the derivative of the second term, y + 8y³, is 1+24y² -4✓ (y + 8y³), we will use the Product Rule, which states 16 y =y-2-4-4, is -4 -5 + 16y−5)(y + 8y³) + (y−² − 4y−4)(1 + 24y² And after expanding the parentheses and simplifying, we conclude that the derivative is as follows.
Transcribed Image Text:Differentiate. Step 1 F(y) ²(x) = (1/27 - 12/2) (X + 8 To find the derivative of the product F(y) = (1/12 - 11/17) (1 Step 2 d [f(y)g(y)] = f'(y)g(y) + f(y)g'(y). dy First, we rewrite the first term of the product as follows. 1 4 V4 The derivative of the first term, -3 F'(y) = Step 4 Now, using the Product Rule, +16 F'(y) = -2 1 4y 4 4 y 1+24y² Step 3 Next, the derivative of the second term, y + 8y³, is 1+24y² -4✓ (y + 8y³), we will use the Product Rule, which states 16 y =y-2-4-4, is -4 -5 + 16y−5)(y + 8y³) + (y−² − 4y−4)(1 + 24y² And after expanding the parentheses and simplifying, we conclude that the derivative is as follows.
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