What is (\partial)/(\partial x)(sin^2(x)cos^2(y)) ?

The answer to (\partial)/(\partial x)(sin^2(x)cos^2(y)) is sin(2x)cos^2(y)

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(\partial)/(\partial x)(sin^2(x)cos^2(y))

\frac{\partial}{\partial x} (sin^{2} (x) cos^{2} (y))

sin (2 x) cos^{2} (y)

Solution steps

\frac{\partial}{\partial x} (sin^{2} (x) cos^{2} (y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= cos^{2} (y) \frac{\partial}{\partial x} (sin^{2} (x))

Apply the chain rule:

2 sin (x) \frac{\partial}{\partial x} (sin (x))

= 2 sin (x) \frac{\partial}{\partial x} (sin (x))

\frac{\partial}{\partial x} (sin (x)) = cos (x)

= cos^{2} (y) \cdot 2 sin (x) cos (x)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 x) cos^{2} (y)

- 3

f (x) = arccos (e^{x})

\int 2 e^{x} - 6 x d x

6 t \frac{d y}{d t} + y = 0

\frac{d}{d x} (\frac{1}{3} sin^{3} (x))

What is (\partial)/(\partial x)(sin^2(x)cos^2(y)) ?
The answer to (\partial)/(\partial x)(sin^2(x)cos^2(y)) is sin(2x)cos^2(y)