Question

$find \: the \: derivative \: of \:$

$4 + {x}^{2}$


$w.r.to \: x$


Answer this irrelevant answers will be reported​

Answer 1

Step-by-step explanation:

Let y=x

x

−2

sinx

Also, let x

x

=u and 2

sinx

=v

∴y=u−v

⇒

dx

dy

=

dx

du

−

dx

dv

u=x

x

Taking logarithm on both the sides, we obtain

logu=xlogx

Differentiating both sides with respect to x, we obtain

u

1

dx

du

=[

dx

d

(x)×logx+x×

dx

d

(logx)]

⇒

dx

du

=u[1×logx+x×

x

1

]

⇒

dx

du

=x

x

(1+logx)

v=2

sinx

Taking logarithm on both the sides with respect to x, we obtain

logv=sinxlog2

Differentiating both sides with respect to x, we obtain

v

1

.

dx

dv

=log2.

dx

d

(sinx)

⇒

dx

dv

=vlog2cosx

⇒

dx

dv

=2

sinx

cosxlog2

∴

dx

dy

=x

x

(1+logx)−2

sinx

cosxlog2