## Important Questions on Differentiation

Q1. **Differentiate the following functions:**

a) **e ^{-x}**

b) **e ^{3x}**

c) **e ^{ax + b}**

d) **e ^{cos x}**

e) **Sin (3x + 5)**

f) **tan ^{2} x**

g) **Sin (log x)**

h) **e ^{tan x}**

i) **Sin ^{2} (2x + 1)**

j) **(log sin x) ^{2}**

Q2. **If x = a (cos t + t sin t)**, **y = a (sin t – t cos t )****find **

Q3. **Differentiate xy = e ^{(x-y)}**

Q5. ** If y = 3 cos (log x) + 4 sin (log x). Show that x ^{2}y_{2} + xy_{1} + y = 0**