Practice Differentiation cont. 112. f(x)

Practice Differentiation cont.
112. f (x) = π x
3
x2
138. f (x) = x sin−1 x +
2
113. f (x) = e(−x
114. f (x) = e(e
137. h(x) = sin−1
x
/2)
139. f (x) =
)
140. f (x) = (ln x)2
141. f (x) = earctan(ln x)
116. r(x) = xe−x
142. f (x) = (ln x)
117. f (x) = 2πe
ln x
163+cos
√
2π
118. f (y) = ln(cos y)
143. p(x) = ln(ln x)
144. g(u) =
119. f (x) = 2x (x3 3x + 2)4
120. g(x) =
eu
eu +1
145. f (x) = x arctan x −
1
2
ln x
2
4
3 −πx
3 πx e
146. h(x) = (2x − 5)(4 − x)−1
147. f (x) = 12 x2 csc x2
121. f (x) = arcsin x
122. f (t) = tt
148. f (θ) = csc−1 (sec θ)
√
123. β(x) = x
x
149. f (z) = sin 3z cos 4z
h
150. f (x) = (x3 + 2)99 +
1/ ln x
124. f (x) = x
125. f (x) = arctan x
126. f (x) = x(e
x
127. f (x) = tan
2/5
128. f (x) = x
Find dy/dx.
)
−1
√
151. x2 y 2 = 1
x
4 x2 +x
2
(x + 3) e
129. f (x) = ln(arccos x)
2
130. f (x) = (arcsin x)
152. x2 − xy + y 3 = 8
√
√
153. x + y + xy = 6
154.
y
x−y
= x2 + 1
155. cos(x − y) = y sin x
131. r(t) = (1 + t2 ) arctan t
156. x cos y + y cos x = 1
132. g(x) = arcsin ex
157. x = tan y
2
133. f (x) = 2(x
+x+1)
158. x + sin y = exy
−x
134. f (x) = ln (3xe
135. α(x) =
1 − x2
1
arcsin(2x)
115. f (x) = sin ex + x5 + sec x
√
√
arctan x
1+x2
136. f (x) = 2sin 3x
)
159. x2/3 + y 2/3 = 1
√
160. xy = 2
sin(x4 )
(x2 −1)3
i7