Find the derivatives of the following :
(i) `(x^(3)3x^(2)+4)(4x^(5)+x^(2)-1)` (ii) `(9x^(2))/(x-3)`

Options

A. `sin 74^(@)`
B. `cos 106^(@)`
C. `sin 15^(@)`
D. `cos 75^(@)`

Answer

D

Explanation

(i) `sin 74^(@)=sin (2xx37^(@))=2 sin 37 cos 37^(@)=2(3/5)(4/5)=24/25`
(ii) `cos 106^(@)=cos (2xx53^(@))=cos^(2) 53^(@)-sin^(2) 53^(@)=(3/5)^(2)-(4/5)^(2)=(9-16)/25=7/25`
(iii) `sin 15^(@)=sin (45^(@)-30^(@))=sin 45^(@) cos 30^(@)-cos 45^(@) sin 30^(@)=1/sqrt(2)xxsqrt(3)/2-1/sqrt(2)xx1/2=(sqrt(3)-1)/(2sqrt(2))`
(iv) `cos 75^(@)=cos(45^(@)+30^(@))=cos 45^(@) cos 30^(@)-sin 45^(@) sin 30^(@)=1/sqrt(2)xxsqrt(3)/2-1/sqrt(2)xx1/2=(sqrt(3)-1)/(2sqrt(2))`