Math 201
Computing Derivatives Name:
Compute the following derivatives. You may use the shortcuts unless otherwise indicated.
(1) Use the limit definition to compute the derivative of f(x) = 2
x−1.
(2) g(x)=3x8−2
x7+√x−6x3+7
x3
(3) h(x)=3ex+ tan(x)−arctan(x) + 9 ln(x)
(4) k(x) = extan(x)
(5) `(x) = exπx
(6) m(x) = 3
√x
5x
(7) n(x) = sin(x)
cos(x)(Does this match with the rule I gave you?)
(8) p(x) = (1 −4x)1000
(9) q(x) = eax
(10) r(x) = esin(x)
(11) s(x) = ln(xj)
(12) t(x) = sec2(x)
(13) u(x) = ln(e2x)
(14) v(x)=6xarctan(13x2)
(15) w(x) = 25x7
ln(cos(x))
(16) z(x) = sin(cos(ln(9x+ 8)))
Use the appropriate parts from above to find the tangent line to the curve at the point indicated.
(1) f(x) at x= 1
(2) k(x) at x=π
4
(3) r(x) at x= 0
(4) u(x) at x= 20
(5) v(x) at x=1
√13
1