Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Calculus - Problems with mixed functions - Differentiation.
 Test Yourself 1.


 
     
Logs and trig functions.

Differentiate:

(i) loge (sin x)

(ii) sin (loge x)

(iii) (logex2 + 2 tan x)2

(iv) cos t × loget

(v) tan a × loge3a

(vi) .

(vi)

 

5. (i) Differentiate loge(cos x) with respect to x.

(ii) Sketch the curve y = tan x
for 0 ≤ x ≤ π/2.

(iii) Hence, using parts (i) and (ii), find the area bounded by the curve y = tan x, the x axis and the line x = π/3.

Leave your answer in the simplest exact form.

  
     
     
Exponential and trig functions.

Differentiate:

(i) .

(ii) x tan x.

 

 

 

 

(v)

Chain    
Product

(i) y = 2x cos (e1.5x)

(ii) e2x tan x.

  

Quotient

(i) .

(ii) .

  
Trig, Log and exponential

Differentiate:

(i) ln (e3x + sin 2x)