16. [0/025 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.5.020. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find dy/dx by implicit differentiation. y 5+X2 tan(x y) = 17. [0/025 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.5.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin(8x) = X cos(2y), (/Z, 71/4) y=0 x Need Help? 4. [0/0.25 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.3.033. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER For what values ofx does the graph off have a horizontal tangent? (Use n as your integer variable. Enter your answers as a comma separated list.) f(x) = X 2 sin(x) 771' x=3 x Need Help? 23. [0/0.25 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.6.020. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. H (z ) = In 12 - 22 d2 + 22 1 H'(Z ) = 2 - 22 2 X d2+ 22 Enhanced Feedback Please try again using the Chain Rule and the differentiation formula [In(g (x ) ) ] = 9( x Keep in mind that In(un) = n In(u), and g ( x ) In = In(a) - In(b).12. [ID/0.25 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.4.053. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (3H, 0) -x Need Help? 20. [-l0.25 Points] DETAILS SCALCET8 3.6.003.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. r(x) = sin(3 |n(x)) f'(x)= Need Help? _'_ 21. [-/0.25 Points] DETAILS SCALCET8 3.6.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. = 5 |n(x) y 22. [0/025 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.6.016. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. y = |n(|3 + t 9\" I3t+t3I x Need Help? 18. [0/0.25 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.5.029. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + y2 = (2x2 + 2y2 - x)2 (0, 0.5) ( cardioid) y = 0.0104 X X Enhanced Feedback :Please try again. In order to find the equation of the tangent line, you first have to find the slope of the tangent line at the given point. To do so, you have to use implicit differentiation. Differentiate both sides with respect to x. Use the Chain Rule or Power Rule when necessary (terms involving y will always need the Chain Rule). Evaluate the terms for the given point (a, b). Let x = a and y = b. Then solve the equation for y'. This will give you the slope of the tangent line. Use the point-slope form to find the equation of the tangent line. Need Help? Watch It28. [0/0.25 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.6.050. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use logarithmic differentiation to find the derivative of the function. y = (In(x)) cos(3x) y' = (In(x) ) Cos (3x ) cos ( 3x) 3 In (x) -3 sin (x ) In (In(x)) x 29. [-/0.25 Points] DETAILS SCALCET8 3.6.510.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find y' and y". y = In(sec(7x) + tan(7x)) y' y" :2. [0/025 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.3.009.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate. 8X y : 3 cot(x) 8(3 c0t(x) xcose2(x)) 3Cot(x)2 Need Help