Question

if y= (sin x²)⁴ , then find dy/dx​

Answer 1

y
=
sin
2
(
x
)
y=sin2(x)
Differentiate both sides of the equation.
d
d
x
(
y
)
=
d
d
x
(
sin
2
(
x
)
)
ddx(y)=ddx(sin2(x))
The derivative of
y
y with respect to
x
x is
y
'
y′.
y
'
y′
Differentiate the right side of the equation.
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2
cos
(
x
)
sin
(
x
)
2cos(x)sin(x)
Reform the equation by setting the left side equal to the right side.
y
'
=
2
cos
(
x
)
sin
(
x
)
y′=2cos(x)sin(x)
Simplify.
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y
'
=
sin
(
2
x
)
y′=sin(2x)
Replace
y
'
y′ with
d
y
d
x
dydx.
d
y
d
x
=
sin
(
2
x
)
dydx=sin(2x)
y
=
s
i
n
2
(
x
)
y=sin2⁡(x)


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