Calculus- Early Transcendentals, 2021a

4.9. Additional Exercises 159
(k) y = tan(sin(x 2 + sec 2 x))
1
(l) y =
2 + sin
x
π
Exercise 4.9.4 Differentiate the following functions.
(a) y = e 3x + e −x + e 2
(b) y = e 2x cos3x
(c) f (x)=tan(x + e x )
(d) g(x)=
ex
e x + 2
(e) y = ln(2 + sinx) − sin(2 + lnx)
(f) f (x)=e xπ + x πe + π ex
(g) y = log a (b x )+b log a x , where a and b are positive real numbers and a ≠ 1.
(h) y =(x 2 + 1) x3 +1
(i) y =(x 2 + e x ) 1/lnx
(j) y =
x √ x 2 + x + 1
(2 + sinx) 4 (3x + 5) 7
Exercise 4.9.5 Find dy if y is a differentiable function that satisfy the given equation.
dx
(a) x 2 + xy + y 2 = 7
(b) x 2 + y 2 =(2x 2 + 2y 2 − x) 2
(c) x 2 siny + y 3 = cosx
(d) x 2 + xe y = 2y + e x
Exercise 4.9.6 Differentiate the following functions.
(a) y = xsin −1 x
(b) f (x)= sin−1 x
cos −1 x
(c) g(x)=tan −1 ( x
a
)
,wherea> 0
(d) y = xtan −1 x − 1 2 ln(x2 + 1)