Question

find the derivative of y=sin^(2)(x)cos^(2)(x)

Answer 1

save time and find the derivative of \(\frac{1}{4}\sin^2(2x)\)

Answer 2

you got this?

Answer 3

Y=[(SIN 2X)/2]^2
Y'= SIN2X(COS2X)(2)

Answer 4

\[\text{Use the product rule, }\frac{d}{dx}(u v)=v \frac{du}{dx}+u \frac{dv}{dx}\text{, where }u=\cos ^2(x)\text{ and }v=\sin ^2(x)\]

Answer 5

you will need to apply chain rule on sin^(2)(x) and cos^(2)(x)
then apply product rule

Answer 6

so
for sin^(2)(x)
g(x) = x^(2) g'(x) = 2x
d(x) = sin(x) d'(x) = cos(x)

thus the derivative of sin^(2)(x) is 2sin(x)cos(x)

for cos^(2)(x)
s(x) = x^(2) s'(x) = 2x
l(x) = cos(x) l'(x) = -sin(x)

thus the derivative of cos^(2)(x) = -2cos(x)sin(x)

Now we apply product rule

f'(x) = 2sin(x)cos(x)cos^(2)(x) + (-2cos(x)sin(x)sin^(2)(x))