Question

d/dx of sin x-x cos x/x sin x + cos x​

Answer 1

Answer:

hope it's helpful to you!

Step-by-step explanation:

Let f(x)=

xsinx+cosx

sinx−xcosx

which is of the form

v

u

f

′

(x)=

v

2

u

′

v−v

′

u

=

(xsinx+cosx)

2

(xsinx+cosx)

dx

d

(sinx−xcosx)−(sinx−xcosx)

dx

d

(xsinx+cosx)

=

(xsinx+cosx)

2

(xsinx+cosx)(cosx−cosx+xsinx)−(sinx−xcosx)(xcosx+sinx−sinx)

=

(xsinx+cosx)

2

(xsinx+cosx)(xsinx)−(sinx−xcosx)(xcosx)

=

(xsinx+cosx)

2

x

2

sin

2

x+xsinxcosx−xsinxcosx+x

2

cos

2

x

=

(xsinx+cosx)

2

x

2

sin

2

x+x

2

cos

2

x

=

(xsinx+cosx)

2

x

2

(sin

2

x+cos

2

x)

=

(xsinx+cosx)

2

x

2

since sin

2

x+cos

2

x=1

hope it's helpful to you!

Answer 2

Answer:

x=1

Step-by-step explanation:

hope this answer will help you