Use implicit differentiation to find

Question

Quizplus · Accepted Answer

Let y = y(x) = 11e^(x^3), then by implicit differentiation, we have:

dy/dx = d/dx(11e^(x^3))
dy/dx = 11e^(x^3) * d/dx(x^3)
dy/dx = 33x^2 * e^(x^3)

So at the point (a3e5_54e9_10a3_9f8f_21ddeb177a8e_TB5971_11, a3e5_54e9_10a4_9f8f_f1cd5910dbda_TB5971_11), we have:

dy/dx = 33(a3e5_54e9_10a3_9f8f_21ddeb177a8e_TB5971_11)^2 * e^[(a3e5_54e9_10a3_9f8f_21ddeb177a8e_TB5971_11)^3]
dy/dx = 33(a3e5_54e9_10a3_9f8f_21ddeb177a8e_TB5971_11)^2 * e^[a3e5_54e9_10a6_9f8f_2542a7844787_TB5971_11]

Substituting back into the equation y = 11e^(x^3), we get:

a3e5_54e9_10a4_9f8f_f1cd5910dbda_TB5971_11 = 11e^(a3e5_54e9_10a3_9f8f_21ddeb177a8e_TB5971_11^3) + (a3e5_54e9_10a4_9f8f_f1cd5910dbda_TB5971_11) * 33(a3e5_54e9_10a3_9f8f_21ddeb177a8e_TB5971_11)^2 * e^[a3e5_54e9_10a6_9f8f_2542a7844787_TB5971_11]

Now, we can solve for a3e5_54e9_10a4_9f8f_f1cd5910dbda_TB5971_11 using numerical methods or a calculator. The approximate value is a3e5_54e9_10a4_9f8f_ef269c16f62b_TB5971_11, which corresponds to choice B.

Use Implicit Differentiation to Find