Question

sin^2x/√cos x differentiate​

Answer 1

d
y
d
x
=
sin
x
(
3
cos
2
x
−
1
)

y
=
(
1
−
cos
2
x
)
cos
x
=
cos
x
−
cos
3
x
We know the derivative of
cos
x
is
−
sin
x
. Letting
y
=
u
3
and
u
=
cos
x
, we have:
(
cos
3
x
)
'
=
−
sin
x
3
u
2
=
−
sin
x
3
(
cos
x
)
2
=
−
3
cos
2
x
sin
x
The derivative of the entire expression is:
d
y
d
x
=
−
sin
x
−
(
−
3
cos
2
x
sin
x
)
d
y
d
x
=
3
cos
2
x
sin
x
−
sin
x
d
y
d
x
=
sin
x
(
3
cos
2
x
−
1
)

Answer 2

Explanation:

Assume base differentiation knowledge: Sin(x) = Cos(x), Cos(x) = -Sin(x)The question combines the chain and product rule. To begin, start by splitting the equation: Sin(2x)Cos(x) = Sin(2x) x Cos(x)The product rule formula is dy/dx = u(dv/dx) + v(du/dx), where in this case u = Sin(2x) and v = Cos