### Home > CALC > Chapter 7 > Lesson 7.1.1 > Problem 7-6

7-6.

Differentiate each equation with respect to

*x*. Leave you answers in terms of only*y*and*x*. Homework Help ✎*y*= 7ln(*x*+ 1) −*x*^{2}2

^{x}^{ }+ 2=^{y}*e**y*=*e*^{tan(}^{x}^{)}(5

*x*+ 1)^{2}+ (*y*+ 1)^{2}= lFind

for part (a). Be sure to leave all parts in terms of *y*and*x*only.Find

for part (a). Write the equation of the tangent line at

*x*= 3 for part (a).Is the tangent line an over or under approximation? Use part (f) to determine your answer.

Chain Rule.

The equation for the tangent line is *y* − *y*(3) = *y*'(3)(*x* − 3).

Implicit Differentiation.

Translation: Evaluate the 2nd-derivative (that you found in part (e)) at *x* = 3.

Is the graph concave up or concave down?