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Derivatives of products and quotients Find the derivative of the following functions by first expanding or simplify the expression. Simplify your answers.
51.
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Chapter 3 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
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- 24x4 – 12x3 6 Find the derivative of: 6x2 Type your answer without negativę exponents. Simplify completely.arrow_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- 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 the first derivative test and the second derivative test to determine where each function is increasing, decreasing, concave up, and concave down. 1 3 y=(9x-3), XER choice. Select the correct choice below and, if necessary, fill in the answer box within your OA. The function is increasing on. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) B. The function is not increasing on any interval.arrow_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 – 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_forwardFind the derivative of the function. 2 + 2arrow_forward3-2x² Find the derivative of y = and simplify your answer. 5x2 +2arrow_forward
- Complete the table to find the derivative of the function. Original Function Rewrite y = 4 3x4 Need Help? Read It 4 3 Watch It -X Differentiate Simplifyarrow_forwardind the derivative of the function using shortcut rules. Simplify for extra credit. g(x) = 5x-3+ 6x-6arrow_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
- Use the first derivative test and the second derivative test to determine where each function is increasing, decreasing, concave up, and concave down. 1 y = (6x - 2)°, xER Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The function is increasing on (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) B. The function is not increasing on any interval.arrow_forwardUse the first derivative test and the second derivative test to determine where each function is increasing, decreasing, concave up, and concave down. 1 3 y = (4x-1) XER Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The function is increasing on (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) OB. The function is not increasing on any interval.arrow_forwarda. Use the Product Rule to find the derivative of the given function. b. Find the derivative by expanding the product first. f(x)equals=left parenthesis x minus 3 right parenthesis left parenthesis 3 x plus 3 right parenthesis(x−3)(3x+3) Question content area bottom Part 1 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. A. The derivative is left parenthesis x minus 3 right parenthesis left parenthesis nothing right parenthesis plus left parenthesis 3 x plus 3 right parenthesis left parenthesis nothing right parenthesis(x−3)enter your response here+(3x+3)enter your response here. B. The derivative is left parenthesis x minus 3 right parenthesis left parenthesis 3 x plus 3 right parenthesis left parenthesis nothing right parenthesis(x−3)(3x+3)enter your response here. C. The derivative is left parenthesis x minus 3 right parenthesis left…arrow_forward
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