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Derivatives of products Find the derivative of the following functions by first expanding the expression. Simplify your answers.
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Chapter 3 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus & Its Applications (14th Edition)
- Determine whether each of the following statements is true or false, and explain why. The derivative of a product is the product of the derivatives.arrow_forward3-2x² Find the derivative of y = and simplify your answer. 5x2 +2arrow_forwardFind the derivative of the function. Simplify and express the answer using positive exponents only. R(x) = [x²(x² + 7x)]ª Step 1 We want to find the derivative of the function R(x) = [x²(x² + 7x)]ª, simplifying and expressing the answer using positive exponents only. We begin by raising both factors inside the brackets to the fourth power. This gives 8 R(x) = x (x2 + 7x) Step 2 We now proceed to take the derivative. Since we rewrote our function as a product of two functions, the first rule we use will be the Product Rule. While using this rule, we will have to also use the Chain Rule. ra) = x* acx² + 7x)*( 4x + 21 D + (x² + 7x)*(8x7) = 4(x2 + 7x)3 4 + (x2 + 7x)2x7 (x² + 7x)³[x(2x + 7) + 2(x2 + 7x)] 4x ( d/dx (x² + 7x)³| x2 + 7 = 4x 11 x+7 3 4х + 21arrow_forward
- Find the derivative of the function. 7 f(x) =3√x X + 6cos x Step 1 Rewrite the function f(x) using an exponential expression for the radical. f(x) = 7x + 6cos x Submit Skin (you cannot come back)arrow_forwardWhich is a correct formula for finding the derivative of the product of two functions a and b? O (ab)'= a'b' (ab)' = a'b + ab' (ab)'= a'+b' Use the correct formula above to find the derivative of the function f(x) = (x³ + 5)√x. Question Help: Message instructor Submit Questionarrow_forwarda. Use the Product Rule to find the derivative of the given function. b. Find the derivative by expanding the product first. f(x) = (x – 4)(5x + 2) a. Use the product rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. O A. The derivative is (x– 4)(5x + 2)(D. O B. The derivative is (x(5x +2). OC. The derivative is (x - 4)(5x+2) + (). O D. The derivative is (x – 4)() + (5x + 2) (). O E. The derivative is ((x-4). Help me solve this View an example Get more help - MacBook Air esc 80 888 F1 F2 F3 F4 F5 F6 F7 @ #3 $ 3 4 6. Q W E Aarrow_forward
- a. Use the Product Rule to find the derivative of the given function. b. Find the derivative by expanding the product first. f(x) = (x- 3)(2x + 3) a. Use the product rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. O A. The derivative is (x - 3)(2x + 3) ( O B. The derivative is (x - 3)() + (2x + 3) () OC. The derivative is () (x- 3). O D. The derivative is ()x(2x+ 3). O E. The derivative is (x- 3)(2x + 3) +arrow_forwardUse differentials to approximate the change in profit corresponding to an increase in sales (or production) of one unit. Then compare this with the actual change in profit. Function x-Value P--0.1x+ 400x - 60 X= 50 dP = dollars dollars Need Help? Read It Watch Itarrow_forwardUse the Product Rule to find the derivative of the function. f(x)= (4x+ 7)(x² 8) а. 8х b. 2x + 4 c. 12x+ 14x- 32 d. 8x2 - 56arrow_forward
- Direction: Find the derivative of each of the following functions. Write your solutions on a separate shee paper. (Rx2) 5. f(x) 4 1 1 b. x² + 16 d. x2 + 16 а. C. (x + 4)2 (x + 4)2arrow_forwardFind the derivative of the function. Express the answer using positive exponents only. y = (x − 9)2(x + 5)arrow_forwardFind the derivative of the function. 8 3 y = √x √√2 -Xarrow_forward
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