Question

Obtain derivatives of the following
functions:
(i) x sin x
(ii) x4+cos x
(iii) x/sin x
​

Answer 1

using multiply rule of derivative

(i)

x‐‐‐i

sinx‐‐- ii

= xcosx +sinx

(ii)x4+cosx

x4-------I

cosx------ii

using addition rule of derivative

derivative of 4x is 4

and cosx is -sinx

then derivative of x4+ cosx is

4–sinx

iii) x/ sinx

using quotient rule x is I

and sinx is ii

sinx–x(–cosx)

sin²x

sinx+xcosx

sin²x

sinx + xcosx

sin²x sin²x

1/sinx+xcosx/sin²x

it may help you

you can understand it easily

Answer 2

Solution:-

ii) Using d/dx [f1(x)+f2 (x)] = df1(x)/d(x) + df2(x)/dx

For f1 (x)=x⁴ and f2 (x)= cosx

d/dx(x⁴+cosx)=d(x⁴)/d+d(cosx)/dx = 4x³- sinx