MA 3972-MA-Book May 9, 2018 10:9Differentiation 1317.9 Practice Problems
Part A The use of a calculator is not allowed.Find the derivative of each of the following
functions.- y= 6 x^5 −x+ 10
- f(x)=
1
x+
1
√ (^3) x 2
- y=
5 x^6 − 1
x^2 - y=
x^2
5 x^6 − 1 - f(x)=(3x−2)^5 (x^2 −1)
- y=
√
2 x+ 1
2 x− 1- y=10 cot(2x−1)
- y= 3 xsec(3x)
- y=10 cos[sin(x^2 −4)]
- y=8 cos−^1 (2x)
- y= 3 e^5 + 4 xex
- y=ln(x^2 +3)
Part B Calculators are allowed.- Find
dy
dx
,ifx^2 +y^3 = 10 − 5 xy. - The graph of a functionf on [1, 5] is
shown in Figure 7.9-1. Find the
approximate value off′(4).
(^0123456)
1
2
3
4
5
6
y
f
x
Figure 7.9-1
- Let fbe a continuous and differentiable
function. Selected values offare shown
below. Find the approximate value of f′at
x=2.
x − 1 0 1 2 3
f 6 5 6 9 14 - If f(x)=x^5 + 3 x−8, find (f−^1 )′(−8).
- Write an equation of the tangent to the
curvey=lnxatx=e. - Ify= 2 xsinx, find
d^2 y
dx^2
atx=
π
2
.
- If the functionf(x)=(x−1)^2 /^3 +2, find all
points wheref is not differentiable. - Write an equation of the normal line to the
curvexcosy=1at
(
2,
π
3)
.- lim
x→ 3
x^2 − 3 x
x^2 − 9- lim
x→ 0 +
ln(x+1)
√
x- lim
x→ 0
ex− 1
tan 2x- lim
x→ 0
cos(x)− 1
cos(2x)− 1- limx→∞
5 x+2lnx
x+3lnx